Sylvester's sequence: Difference between revisions
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{{
{{Wikipedia|Sylvester's sequence}}
In number theory,
Its values grow doubly exponentially,
Further, the sum of the first
Line 13:
* Write a routine (function, procedure, generator, whatever) to calculate '''Sylvester's sequence'''.
* Use that routine to show the values of the first '''10''' elements in the sequence.
* Show the sum of the reciprocals of the first '''10''' elements on the sequence
;Related tasks:
;See also:
=={{header|11l}}==
{{trans|Nim}}
<syntaxhighlight lang="11l">F sylverster(lim)
V result = [BigInt(2)]
L 2..lim
result.append(product(result) + 1)
R result
V l = sylverster(10)
print(‘First 10 terms of the Sylvester sequence:’)
L(item) l
print(item)
V s = 0.0
L(item) l
s += 1 / Float(item)
print("\nSum of the reciprocals of the first 10 terms: #.17".format(s))</syntaxhighlight>
{{out}}
<pre>
First 10 terms of the Sylvester sequence:
2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Sum of the reciprocals of the first 10 terms: 0.99999999999999982
</pre>
=={{header|ALGOL 68}}==
{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}}
Uses Algol 68G's LONG LONG INT and LONG LONG REAL which have specifiable precision. The sum of the reciprocals in the output has been manually edited to replace a large number of nines with ... to reduce the width.
<
PR precision 200 PR # set the number of digits for LONG LONG modes #
# returns an array set to the forst n elements of Sylvestor's Sequence #
Line 54 ⟶ 90:
print( ( "Sum of reciprocals: ", reciprocal sum, newline ) )
END
</syntaxhighlight>
{{out}}
<pre>
Line 72 ⟶ 108:
=={{header|Arturo}}==
<
result: new [2]
loop 2..lim 'x [
Line 88 ⟶ 124:
print "Sum of the reciprocals of the first 10 items:"
print sumRep</
{{out}}
Line 97 ⟶ 133:
Sum of the reciprocals of the first 10 items:
1.0</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK --bignum -f SYLVESTERS_SEQUENCE.AWK
BEGIN {
start = 1
stop = 10
for (i=start; i<=stop; i++) {
sylvester = (i == 1) ? 2 : sylvester*sylvester-sylvester+1
printf("%2d: %d\n",i,sylvester)
sum += 1 / sylvester
}
printf("\nSylvester sequence %d-%d: sum of reciprocals %30.28f\n",start,stop,sum)
exit(0)
}
</syntaxhighlight>
{{out}}
<pre>
1: 2
2: 3
3: 7
4: 43
5: 1807
6: 3263443
7: 10650056950807
8: 113423713055421844361000443
9: 12864938683278671740537145998360961546653259485195807
10: 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Sylvester sequence 1-10: sum of reciprocals 0.9999999999999998889776975375
</pre>
=={{header|BASIC}}==
Line 104 ⟶ 169:
{{works with|Chipmunk Basic}}
{{trans|FreeBASIC}}
<
PRINT "10 primeros términos de la sucesión de sylvester:"
PRINT
Line 122 ⟶ 187:
PRINT "suma de sus recíprocos: "; suma
END
</syntaxhighlight>
==={{header|FreeBASIC}}===
'''precisión estándar'''
<
Dim As Double sylvester, suma = 0
Line 140 ⟶ 205:
Print !"\nSuma de sus rec¡procos:"; suma
Sleep
</syntaxhighlight>
{{out}}
<pre>
Line 160 ⟶ 225:
==={{header|PureBasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="purebasic">
OpenConsole()
PrintN("10 primeros términos de la sucesión de Sylvester:")
Line 179 ⟶ 244:
CloseConsole()
End
</syntaxhighlight>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<
print "10 primeros términos de la sucesión de Sylvester:"
Line 195 ⟶ 260:
print "\nSuma de sus rec¡procos: ", suma
end
</syntaxhighlight>
=={{header|C#}}==
{{trans|Go}}
<syntaxhighlight lang="C#">
using System;
using System.Collections.Generic;
using System.Numerics;
public class SylvesterSequence
{
public static void Main(string[] args)
{
BigInteger one = BigInteger.One;
BigInteger two = new BigInteger(2);
List<BigInteger> sylvester = new List<BigInteger> { two };
BigInteger prod = two;
int count = 1;
while (count < 10)
{
BigInteger next = BigInteger.Add(prod, one);
sylvester.Add(next);
count++;
prod *= next;
}
Console.WriteLine("The first 10 terms in the Sylvester sequence are:");
foreach (var term in sylvester)
{
Console.WriteLine(term);
}
// Assuming a BigRational implementation or a workaround for the sum of reciprocals
BigInteger denominator = BigInteger.One;
foreach (var term in sylvester)
{
denominator = BigInteger.Multiply(denominator, term);
}
BigInteger numerator = BigInteger.Zero;
foreach (var term in sylvester)
{
numerator += denominator / term;
}
// Assuming you have a way to convert this to a decimal representation
Console.WriteLine("\nThe sum of their reciprocals as a rational number is:");
Console.WriteLine($"{numerator}/{denominator}");
// For the decimal representation, you might need to perform the division to a fixed number of decimal places
// This is a simplified approach and may not directly achieve 211 decimal places accurately
Console.WriteLine("\nThe sum of their reciprocals as a decimal number (to 211 places) is:");
Console.WriteLine(DecimalDivide(numerator, denominator, 210));
}
private static string DecimalDivide(BigInteger numerator, BigInteger denominator, int decimalPlaces)
{
// This is a basic implementation and might not be accurate for very large numbers or very high precision requirements
BigInteger quotient = BigInteger.Divide(numerator * BigInteger.Pow(10, decimalPlaces + 1), denominator);
string quotientStr = quotient.ToString();
string result = quotientStr.Substring(0, quotientStr.Length - decimalPlaces) + "." + quotientStr.Substring(quotientStr.Length - decimalPlaces);
return result;
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 10 terms in the Sylvester sequence are:
2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
The sum of their reciprocals as a rational number is:
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
The sum of their reciprocals as a decimal number (to 211 places) is:
9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999634
</pre>
=={{header|C++}}==
{{libheader|Boost}}
<
#include <iostream>
#include <boost/rational.hpp>
Line 222 ⟶ 373:
}
std::cout << "Sum of reciprocals: " << sum << '\n';
}</
{{out}}
Line 239 ⟶ 390:
Sum of reciprocals: 27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
numfmt 8 0
for i = 1 to 10
if i = 1
sylv = 2
else
sylv = sylv * sylv - sylv + 1
.
print sylv
sum += 1 / sylv
.
print ""
print sum
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
<
// Sylvester's sequence: Nigel Galloway. June 7th., 2021
let S10=Seq.unfold(fun(n,g)->printfn "*%A %A" n g; Some(n,(n*g+1I,n*g) ) )(2I,1I)|>Seq.take 10|>List.ofSeq
S10|>List.iteri(fun n g->printfn "%2d -> %A" (n+1) g)
let n,g=S10|>List.fold(fun(n,g) i->(n*i+g,g*i))(0I,1I) in printfn "\nThe sum of the reciprocals of S10 is \n%A/\n%A" n g
</syntaxhighlight>
{{out}}
<pre>
Line 269 ⟶ 436:
{{works with|Factor|0.99 2021-02-05}}
<
: lsylvester ( -- list ) 2 [ dup sq swap - 1 + ] lfrom-by ;
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"Sum of the reciprocals of first 10 elements:" print
0 [ recip + ] foldl .</
{{out}}
<pre>
Line 297 ⟶ 464:
Or, in other words, the sum is <code>2739245…392080'''5/'''2739245…392080'''6'''</code>.
=={{header|Fermat}}==
<syntaxhighlight lang="fermat">Array syl[10];
syl[1]:=2;
for i=2 to 10 do syl[i]:=1+Prod<n=1,i-1>[syl[n]] od;
!![syl];
srec:=Sigma<i=1,10>[1/syl[i]];
!!srec;</syntaxhighlight>
{{out}}<pre>
syl[1] := 2
syl[2] := 3
syl[3] := 7
syl[4] := 43
syl[5] := 1807
syl[6] := 3263443
syl[7] := 10650056950807
syl[8] := 113423713055421844361000443
syl[9] := 12864938683278671740537145998360961546653259485195807
syl[10] := 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
2739245030860303142341023429167468628119436436758091462794736794160869202622699363433211840458243863492954873728399236975 `
8487974306317730580753883429460344956410077034761330476016739454649828385541500213920805 / 273924503086030314234102342916746 `
862811943643675809146279473679416086920262269936343321184045824386349295487372839923697584879743063177305807538834294603 `
44956410077034761330476016739454649828385541500213920806
</pre>
=={{header|Go}}==
{{trans|Wren}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"math/big"
)
func main() {
one := big.NewInt(1)
two := big.NewInt(2)
next := new(big.Int)
sylvester := []*big.Int{two}
prod := new(big.Int).Set(two)
count := 1
for count < 10 {
next.Add(prod, one)
sylvester = append(sylvester, new(big.Int).Set(next))
count++
prod.Mul(prod, next)
}
fmt.Println("The first 10 terms in the Sylvester sequence are:")
for i := 0; i < 10; i++ {
fmt.Println(sylvester[i])
}
sumRecip := new(big.Rat)
for _, s := range sylvester {
sumRecip.Add(sumRecip, new(big.Rat).SetFrac(one, s))
}
fmt.Println("\nThe sum of their reciprocals as a rational number is:")
fmt.Println(sumRecip)
fmt.Println("\nThe sum of their reciprocals as a decimal number (to 211 places) is:")
fmt.Println(sumRecip.FloatString(211))
}</syntaxhighlight>
{{out}}
<pre>
The first 10 terms in the Sylvester sequence are:
2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
The sum of their reciprocals as a rational number is:
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
The sum of their reciprocals as a decimal number (to 211 places) is:
0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999635
</pre>
=={{header|Haskell}}==
<
sylvester = map s [0 ..]
where
Line 314 ⟶ 565:
putStr "Sum of reciprocals by fold: "
print $ foldr ((+) . (1 /) . fromInteger) 0 $ take 10 sylvester</
{{out}}
<pre>First 10 elements of Sylvester's sequence:
Line 332 ⟶ 583:
Simpler way of generating sequence:
<
sylvester = iterate (\x -> x * (x-1) + 1) 2</
or applicatively:
<
sylvester = iterate (succ . ((*) <*> pred)) 2</
=={{header|J}}==
J uses r instead of / to display rationals
<syntaxhighlight lang="j"> 2 ('Sum of reciprocals: ' , ":@:(+/))@:%@:([ echo&>)@:((, 1x + */)@[&_~) 9
2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Sum of reciprocals: 27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805r27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806</syntaxhighlight>
=={{header|jq}}==
<
def sylvester:
foreach range(0; infinite) as $i ({prev: 1, product: 1};
.product *= .prev
| .prev = .product + 1;
.prev);</
Left padding:
<syntaxhighlight lang="jq">
def lpad($len; $fill): tostring | ($len - length) as $l | ($fill * $l)[:$l] + .;
def lpad($len): lpad($len; " ");
def lpad: lpad(4);</
The task:
<
| "First 10 Sylvester numbers:",
(range(0;10) as $i | "\($i+1|lpad) => \(.[$i])"),
"",
"Sum of reciprocals of first 10 is approximately: \(map( 1/ .) | add)"
</syntaxhighlight>
{{out}}
For integer precision, we will use `gojq`, the "go" implementation of jq.
Line 376 ⟶ 643:
=={{header|Julia}}==
<
foreach(n -> println(rpad(n, 3), " => ", sylvester(n)), 1:10)
println("Sum of reciprocals of first 10: ", sum(big"1.0" / sylvester(n) for n in 1:10))
</
<pre>
1 => 2
Line 395 ⟶ 662:
Sum of reciprocals of first 10: 0.9999999999999999999999999999999999999999999999999999999999999999999999999999914
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Rest[Nest[Append[#, (Times @@ #) + 1] &, {1}, 10]]
N[Total[1/%], 250]</syntaxhighlight>
{{out}}
<pre>{2,3,7,43,1807,3263443,10650056950807,113423713055421844361000443,12864938683278671740537145998360961546653259485195807,165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443}
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996349359079841301329356159748234615361531272</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
sylvester[n]:= if n=0 then sylvester[n]:2 else sylvester[n-1]^2-sylvester[n-1]+1$
/* Test cases */
makelist(sylvester[i],i,0,9);
apply("+",1/%);
</syntaxhighlight>
{{out}}
<pre>
[2,3,7,43,1807,3263443,10650056950807,113423713055421844361000443,12864938683278671740537145998360961546653259485195807,165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443]
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
</pre>
=={{header|Nim}}==
{{libheader|bignum}}
<
import bignum
Line 413 ⟶ 703:
var sum = newRat()
for item in list: sum += newRat(1, item)
echo "\nSum of the reciprocals of the first 10 terms: ", sum.toFloat</
{{out}}
Line 429 ⟶ 719:
Sum of the reciprocals of the first 10 terms: 0.9999999999999999</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">
S=vector(10)
S[1]=2
for(i=2, 10, S[i]=prod(n=1,i-1,S[n])+1)
print(S)
print(sum(i=1,10,1/S[i]))</syntaxhighlight>
{{out}}<pre>[2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807, 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443]
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
</pre>
=={{header|Pascal}}==
{{works with|Free Pascal}}
Free Pascal console program, using the library IntXLib4Pascal for arbitrarily large integers. I couldn't get the library to work with Delphi 7; it's said to work with Delphi 2010 and above.
<syntaxhighlight lang="pascal">
program SylvesterSeq;
{$mode objfpc}{$H+}
uses SysUtils,
UIntX; // in the library IntX4Pascal
(*
As noted in the Wikipedia article "Sylvester's sequence", we have
1/2 + 1/3 + ... + 1/s[j-1] = (s[j] - 2)/(s[j] - 1),
so that instead of summing the reciprocals explicitly we can just
calculate an extra term.
*)
var
s : UIntX.TIntX; // arbitrarily large integer
i : integer;
begin
s := 1;
for i := 0 to 9 do begin
inc(s);
WriteLn( SysUtils.Format( 's[%d] = %s', [i, s.ToString]));
s := s*(s - 1);
end;
WriteLn( 'Sum of reciprocals =');
WriteLn( (s - 1).ToString);
WriteLn( '/'); // on a separate line for clarity
WriteLn( s.ToString);
end.
</syntaxhighlight>
{{out}}
<pre>
s[0] = 2
s[1] = 3
s[2] = 7
s[3] = 43
s[4] = 1807
s[5] = 3263443
s[6] = 10650056950807
s[7] = 113423713055421844361000443
s[8] = 12864938683278671740537145998360961546653259485195807
s[9] = 1655066473245199641984681954444391800175131527063774978418513887665358686
39572406808911988131737645185443
Sum of reciprocals =
27392450308603031423410234291674686281194364367580914627947367941608692026226993
63433211840458243863492954873728399236975848797430631773058075388342946034495641
0077034761330476016739454649828385541500213920805
/
27392450308603031423410234291674686281194364367580914627947367941608692026226993
63433211840458243863492954873728399236975848797430631773058075388342946034495641
0077034761330476016739454649828385541500213920806
</pre>
=={{header|Perl}}==
<
use warnings;
use feature 'say';
Line 444 ⟶ 802:
say "First 10 elements of Sylvester's sequence: @S";
say "\nSum of the reciprocals of first 10 elements: " . float $sum;</
{{out}}
<pre>First 10 elements of Sylvester's sequence: 2 3 7 43 1807 3263443 10650056950807 113423713055421844361000443 12864938683278671740537145998360961546653259485195807 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Line 452 ⟶ 810:
=={{header|Phix}}==
=== standard precision ===
<!--<
<span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">32</span><span style="color: #0000FF;">?</span><span style="color: #000000;">53</span><span style="color: #0000FF;">:</span><span style="color: #000000;">64</span><span style="color: #0000FF;">))</span>
Line 461 ⟶ 819:
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sum of reciprocals: %g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">})</span>
<!--</
{{out}}
<pre>
Line 478 ⟶ 836:
=== mpfr version ===
Note the (minimal) precision settings of 698 and 211 were found by trial and error (ie larger values gain nothing but smaller ones lose accuracy).
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.0"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (mpfr_set_default_prec[ision] has been renamed)
Line 498 ⟶ 856:
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sum of reciprocals: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">211</span><span style="color: #0000FF;">))})</span>
<!--</
{{out}}
<pre>
Line 518 ⟶ 876:
<br>It doesn't calculate the reciprocal sum as 8080 PL/M has no floating point...
<br>This sample can be compiled with the original 8080 PL/M compiler and run under CP/M (or an emulator or clone).
<
BDOS: PROCEDURE( FN, ARG ); /* CP/M BDOS SYSTEM CALL */
Line 638 ⟶ 996:
CALL PRINT$LONG$INTEGER( .PRODUCT );
CALL PRINT$NL;
EOF</
{{out}}
<pre>
Line 655 ⟶ 1,013:
=={{header|Prolog}}==
{{works with|SWI Prolog}}
<
sylvesters_sequence(N, S, 2, R, 0).
Line 673 ⟶ 1,031:
N is numerator(Sum),
D is denominator(Sum),
writef('\nSum of reciprocals: %t / %t\n', [N, D]).</
{{out}}
Line 694 ⟶ 1,052:
=={{header|Python}}==
<
from functools import reduce
Line 735 ⟶ 1,093:
# MAIN ---
if __name__ == '__main__':
main()</
{{Out}}
<pre>First 10 terms of OEIS A000058:
Line 751 ⟶ 1,109:
Sum of the reciprocals of the first 10 terms:
0.9999999999999999</pre>
Or as an iteration:
<syntaxhighlight lang="python">'''Sylvester's sequence'''
from functools import reduce
from itertools import islice
# sylvester :: [Int]
def sylvester():
'''A non finite sequence of the terms of OEIS A000058
'''
return iterate(
lambda x: x * (x - 1) + 1
)(2)
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''First terms, and sum of reciprocals.'''
print("First 10 terms of OEIS A000058:")
xs = list(islice(sylvester(), 10))
print('\n'.join([
str(x) for x in xs
]))
print("\nSum of the reciprocals of the first 10 terms:")
print(
reduce(lambda a, x: a + 1 / x, xs, 0)
)
# ----------------------- GENERIC ------------------------
# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''
def go(x):
v = x
while True:
yield v
v = f(v)
return go
# MAIN ---
if __name__ == '__main__':
main()</syntaxhighlight>
{{Out}}
<pre>First 10 terms of OEIS A000058:
2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Sum of the reciprocals of the first 10 terms:
0.9999999999999999</pre>
=={{header|Quackery}}==
<syntaxhighlight lang="quackery">[ $ "bigrat.qky" loadfile ] now!
' [ 2 ] 9 times [ dup -1 peek dup 2 ** swap - 1+ join ]
dup witheach [ echo cr ] cr
0 n->v rot witheach [ n->v 1/v v+ ] 222 point$ echo$</syntaxhighlight>
{{out}}
The first 222 digits after the decimal point are shown for the sum of reciprocals.
<pre>2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999963493590798413
</pre>
=={{header|Raku}}==
<syntaxhighlight lang="raku"
put 'First 10 elements of Sylvester\'s sequence: ', @S[^10];
say "\nSum of the reciprocals of first 10 elements: ", sum @S[^10].map: { FatRat.new: 1, $_ };</
{{out}}
<pre>First 10 elements of Sylvester's sequence: 2 3 7 43 1807 3263443 10650056950807 113423713055421844361000443 12864938683278671740537145998360961546653259485195807 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Line 764 ⟶ 1,214:
=={{header|REXX}}==
<
parse arg n . /*obtain optional argument from the CL.*/
if n=='' | n=="," then n= 10 /*Not specified? Then use the default.*/
Line 777 ⟶ 1,227:
say /*stick a fork in it, we're all done. */
numeric digits digits() - 1
say 'sum of the first ' n " reciprocals using" digits() 'decimal digits: ' $ / 1</
{{out|output|text= when using the default inputs:}}
<pre>
Line 794 ⟶ 1,244:
</pre>
=={{header|RPL}}==
{{works with|HP|49}}
≪ { 2 3 }
'''DO'''
DUP ΠLIST 1 + +
'''UNTIL''' DUP2 SIZE == '''END'''
NIP
≫ '<span style="color:blue">SYLV</span>' STO
10 <span style="color:blue">SYLV</span>
DUP INV ∑LIST EXPAND
{{out}}
<pre>
2: { 2 3 7 43 1807 3263443 10650056950807 113423713055421844361000443 12864938683278671740537145998360961546653259485195807 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443 }
1: 27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805 /
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">def sylvester(n) = (1..n).reduce(2){|a| a*a - a + 1 }
(0..9).each {|n| puts "#{n}: #{sylvester n}" }
puts "
Sum of reciprocals of first 10 terms:
#{(0..9).sum{|n| 1.0r / sylvester(n)}.to_f }"
</syntaxhighlight>
{{out}}
<pre>0: 2
1: 3
2: 7
3: 43
4: 1807
5: 3263443
6: 10650056950807
7: 113423713055421844361000443
8: 12864938683278671740537145998360961546653259485195807
9: 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Sum of reciprocals of first 10 terms:
1.0
</pre>
=={{header|Scheme}}==
<syntaxhighlight lang="scheme">(define sylvester
(lambda (x)
(if (= x 1)
2
(let ((n (sylvester (- x 1)))) (- (* n n) n -1)))))
(define list (map sylvester '(1 2 3 4 5 6 7 8 9 10)))
(print list)
(newline)
(print (apply + (map / list)))</syntaxhighlight>
{{out}}
<pre>
(2 3 7 43 1807 3263443 10650056950807 113423713055421844361000443 12864938683278671740537145998360961546653259485195807 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443)
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
</pre>
=={{header|Seed7}}==
<
include "bigint.s7i";
include "bigrat.s7i";
Line 816 ⟶ 1,323:
writeln("\nSum of the reciprocals of the first 10 elements:");
writeln(reciprocalSum digits 210);
end func;</
{{out}}
<pre>
Line 836 ⟶ 1,343:
=={{header|Sidef}}==
<
1..n -> reduce({|a| a*(a-1) + 1 }, 2)
}
Line 844 ⟶ 1,351:
say "\nSum of reciprocals of first 10 terms: "
say 10.of(sylvester_sequence).sum {|n| 1/n }.as_dec(230)</
{{out}}
Line 864 ⟶ 1,371:
</pre>
=={{header|Swift}}==
Using mkrd's BigNumber library.
<syntaxhighlight lang="swift">import BigNumber
func sylvester(n: Int) -> BInt {
var a = BInt(2)
for _ in 0..<n {
a = a * a - a + 1
}
return a
}
var sum = BDouble(0)
for n in 0..<10 {
let syl = sylvester(n: n)
sum += BDouble(1) / BDouble(syl)
print(syl)
}
print("Sum of the reciprocals of first ten in sequence: \(sum)")</syntaxhighlight>
{{out}}
<pre>2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
Sum of the reciprocals of first ten in sequence: 27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806</pre>
=={{header|Verilog}}==
<syntaxhighlight lang="verilog">
module main;
integer i;
Line 890 ⟶ 1,436:
end
endmodule
</syntaxhighlight>
{{out}}
<pre>10 primeros términos de la sucesión de sylvester:
Line 910 ⟶ 1,456:
=={{header|Wren}}==
{{libheader|Wren-big}}
<
var sylvester = [BigInt.two]
Line 929 ⟶ 1,475:
System.print (sumRecip)
System.print("\nThe sum of their reciprocals as a decimal number (to 211 places) is:")
System.print(sumRecip.toDecimal(211))</
{{out}}
| |||