Disarium numbers
A Disarium number is an integer where the sum of each digit raised to the power of its position in the number, is equal to the number.
- E.G.
135 is a Disarium number:
11 + 32 + 53 == 1 + 9 + 125 == 135
There are a finite number of Disarium numbers.
- Task
- Find and display the first 18 Disarium numbers.
- Stretch
- Find and display all 20 Disarium numbers.
- See also
- Geeks for Geeks - Disarium numbers
- OEIS:A032799 - Numbers n such that n equals the sum of its digits raised to the consecutive powers (1,2,3,...)
- Related task: Narcissistic decimal number
- Related task: Own digits power sum Which seems to be the same task as Narcissistic decimal number...
Factor
<lang factor>USING: io kernel lists lists.lazy math.ranges math.text.utils math.vectors prettyprint sequences ;
- disarium? ( n -- ? )
dup 1 digit-groups dup length 1 [a,b] v^ sum = ;
- disarium ( -- list ) 0 lfrom [ disarium? ] lfilter ;
19 disarium ltake [ pprint bl ] leach nl</lang>
- Output:
0 1 2 3 4 5 6 7 8 9 89 135 175 518 598 1306 1676 2427 2646798
BASIC
BASIC256
<lang freebasic>function isDisarium(n) digitos = length(string(n)) suma = 0 x = n while x <> 0 suma += (x % 10) ^ digitos digitos -= 1 x = x \ 10 end while if suma = n then return True else return False end function
limite = 19 cont = 0 : n = 0 print "The first"; limite; " Disarium numbers are:" while cont < limite if isDisarium(n) then print n; " "; cont += 1 endif n += 1 end while end</lang>
- Output:
Igual que la entrada de FreeBASIC.
FreeBASIC
<lang freebasic>#define limite 19
Function isDisarium(n As Integer) As Boolean
Dim As Integer digitos = Len(Str(n))
Dim As Integer suma = 0, x = n
While x <> 0
suma += (x Mod 10) ^ digitos
digitos -= 1
x \= 10
Wend
Return Iif(suma = n, True, False)
End Function
Dim As Integer cont = 0, n = 0, i Print "The first"; limite; " Disarium numbers are:" Do While cont < limite
If isDisarium(n) Then
Print n; " ";
cont += 1
End If
n += 1
Loop Sleep</lang>
- Output:
Igual que la entrada de Python.
PureBasic
<lang PureBasic>Procedure isDisarium(n.i)
digitos.i = Len(Str(n)) suma.i = 0 x.i = n While x <> 0 r.i = (x % 10) suma + Pow(r, digitos) digitos - 1 x / 10 Wend If suma = n ProcedureReturn #True Else ProcedureReturn #False EndIf
EndProcedure
OpenConsole() limite.i = 19 cont.i = 0 n.i = 0 PrintN("The first" + Str(limite) + " Disarium numbers are:") While cont < limite
If isDisarium(n) Print(Str(n) + #TAB$) cont + 1 EndIf n + 1
Wend Input() CloseConsole()</lang>
- Output:
Igual que la entrada de FreeBASIC.
Julia
<lang julia>isdisarium(n) = sum(last(p)^first(p) for p in enumerate(reverse(digits(n)))) == n
function disariums(numberwanted)
n, ret = 0, Int[]
while length(ret) < numberwanted
isdisarium(n) && push!(ret, n)
n += 1
end
return ret
end
println(disariums(19)) @time disariums(19)
</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427, 2646798] 0.555962 seconds (5.29 M allocations: 562.335 MiB, 10.79% gc time)
Perl
<lang perl>use strict; use warnings;
my ($n,@D) = (0, 0); while (++$n) {
my($m,$sum);
map { $sum += $_ ** ++$m } split , $n;
push @D, $n if $n == $sum;
last if 19 == @D;
} print "@D\n";</lang>
- Output:
0 1 2 3 4 5 6 7 8 9 89 135 175 518 598 1306 1676 2427 2646798
Phix
with javascript_semantics constant limit = 19 integer count = 0, n = 0 printf(1,"The first 19 Disarium numbers are:\n") while count<limit do atom dsum = 0 string digits = sprintf("%d",n) for i=1 to length(digits) do dsum += power(digits[i]-'0',i) end for if dsum=n then printf(1," %d",n) count += 1 end if n += 1 end while
- Output:
The first 19 Disarium numbers are: 0 1 2 3 4 5 6 7 8 9 89 135 175 518 598 1306 1676 2427 2646798
stretch
with javascript_semantics -- translation of https://github.com/rgxgr/Disarium-Numbers/blob/master/Disarium.c constant DMAX = iff(machine_bits()=64?20:7) // Pre-calculated exponential & power serials sequence exps = repeat(repeat(0,11),1+DMAX), pows = repeat(repeat(0,11),1+DMAX) exps[1..2] = {{0,0,0,0,0,0,0,0,0,0,1},{0,1,2,3,4,5,6,7,8,9,10}} pows[1..2] = {{0,0,0,0,0,0,0,0,0,0,0},{0,1,2,3,4,5,6,7,8,9, 9}} for i=2 to DMAX do for j=1 to 10 do exps[i+1][j] = exps[i][j]*10 pows[i+1][j] = pows[i][j]*(j-1) end for exps[i+1][11] = exps[i][11]*10 pows[i+1][11] = pows[i][11] + pows[i+1][10] end for // Digits of candidate and values of known low bits sequence digits = repeat(0,1+DMAX), // Digits form expl = repeat(0,1+DMAX), // Number form powl = repeat(0,1+DMAX) // Powers form printf(1,"") -- (exclude console setup from timings [if pw.exe]) atom expn, powr, minn, maxx, t0 = time(), t1 = t0+1, count = 0 for digit=2 to DMAX+1 do printf(1,"Searching %d digits (started at %s):\n", {digit-1,elapsed(time()-t0)}); integer level = 2 digits[1] = 0 while true do // Check limits derived from already known low bit values // to find the most possible candidates while 1<level and level<digit do // Reset path to try next if checking in level is done integer dl = digits[level]+1 if dl>10 then digits[level] = 0; level -= 1 digits[level] += 1 else // Update known low bit values expl[level] = expl[level-1] + exps[level][dl] powl[level] = powl[level-1] + pows[digit-level+2][dl] // Max possible value powr = powl[level] + pows[digit-level+1][11] atom ed2 = exps[digit][2] if powr<ed2 then // Try next since upper limit is invalidly low digits[level] += 1 else atom el11 = exps[level][11], el = expl[level] maxx = remainder(powr,el11) powr -= maxx if maxx<el then powr -= el11 end if maxx = powr + el if maxx<ed2 then // Try next since upper limit is invalidly low digits[level] += 1 else // Min possible value expn = el + ed2 powr = powl[level] + 1 if expn>maxx or maxx<powr then // Try next since upper limit is invalidly low digits[level] += 1 else if powr>expn then minn = remainder(powr,el11) powr -= minn if minn>el then powr += el11 end if minn = powr + el else minn = expn end if // Check limits existence if maxx<minn then digits[level] +=1 // Try next number since current limits invalid else level +=1 // Go for further level checking since limits available end if end if end if end if end if if time()>t1 and platform()!=JS then progress("working:%v... (%s)",{digits,elapsed(time()-t0)}) t1 = time()+1 end if end while // All checking is done, escape from the main check loop if level<2 then exit end if // Final check last bit of the most possible candidates // Update known low bit values integer dlx = digits[level]+1 expl[level] = expl[level-1] + exps[level][dlx]; powl[level] = powl[level-1] + pows[digit+1-level][dlx]; // Loop to check all last bit of candidates while digits[level]<10 do // Print out new disarium number if expl[level] == powl[level] then if platform()!=JS then progress("") end if integer ld = max(trim_tail(digits,0,true),2) printf(1,"%s\n",{reverse(join(apply(digits[2..ld],sprint),""))}) count += 1 end if // Go to followed last bit candidate digits[level] += 1 expl[level] += exps[level][2] powl[level] += 1 end while // Reset to try next path digits[level] = 0; level -= 1 digits[level] += 1 end while if platform()!=JS then progress("") end if end for printf(1,"%d disarium numbers found (%s)\n",{count,elapsed(time()-t0)})
- Output:
Searching 1 digits (started at 0s): 0 1 2 3 4 5 6 7 8 9 Searching 2 digits (started at 0s): 89 Searching 3 digits (started at 0s): 135 175 518 598 Searching 4 digits (started at 0s): 1306 1676 2427 Searching 5 digits (started at 0.0s): Searching 6 digits (started at 0.0s): Searching 7 digits (started at 0.0s): 2646798 Searching 8 digits (started at 0.0s): Searching 9 digits (started at 0.0s): Searching 10 digits (started at 0.0s): Searching 11 digits (started at 0.1s): Searching 12 digits (started at 0.1s): Searching 13 digits (started at 0.3s): Searching 14 digits (started at 0.8s): Searching 15 digits (started at 2.5s): Searching 16 digits (started at 6.9s): Searching 17 digits (started at 23.2s): Searching 18 digits (started at 1 minute and 8s): Searching 19 digits (started at 3 minutes and 35s): Searching 20 digits (started at 10 minutes and 8s): 12157692622039623539 20 disarium numbers found (2 hours and 7s)
Takes about 48min to find the 20 digit number, then trundles away for over another hour. I think that technically it should also scan for 21 and 22 digit numbers to be absolutely sure there aren't any, but that certainly exceeds my patience.
Python
<lang python>#!/usr/bin/python
def isDisarium(n):
digitos = len(str(n))
suma = 0
x = n
while x != 0:
suma += (x % 10) ** digitos
digitos -= 1
x //= 10
if suma == n:
return True
else:
return False
if __name__ == '__main__':
limite = 19
cont = 0
n = 0
print("The first",limite,"Disarium numbers are:")
while cont < limite:
if isDisarium(n):
print(n, end = " ")
cont += 1
n += 1</lang>
- Output:
The first 19 Disarium numbers are: 0 1 2 3 4 5 6 7 8 9 89 135 175 518 598 1306 1676 2427 2646798
Raku
Not an efficient algorithm. First 18 in less than 1/4 second. 19th in around 45 seconds. Pretty much unusable for the 20th. <lang perl6>my $disarium = (^∞).hyper.map: { $_ if $_ == sum .polymod(10 xx *).reverse Z** 1..* };
put $disarium[^18]; put $disarium[18];</lang>
- Output:
0 1 2 3 4 5 6 7 8 9 89 135 175 518 598 1306 1676 2427 2646798
Wren
Version 1 (Brute force)
This version finds the first 19 Disarium numbers in 3.35 seconds though, clearly, finding the 20th is out of the question with this approach.
As a possible optimization, I tried caching all possible digit powers but there was no perceptible difference in running time for numbers up to 7 digits long. <lang ecmascript>import "./math" for Int
var limit = 19 var count = 0 var disarium = [] var n = 0 while (count < limit) {
var sum = 0
var digits = Int.digits(n)
for (i in 0...digits.count) sum = sum + digits[i].pow(i+1)
if (sum == n) {
disarium.add(n)
count = count + 1
}
n = n + 1
} System.print("The first 19 Disarium numbers are:") System.print(disarium)</lang>
- Output:
The first 19 Disarium numbers are: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427, 2646798]
Version 2 (Much faster)
This is a translation of the C code referred to in the Phix entry and finds the first 19 Disarium numbers in 0.012 seconds.
Efficient though this method is, unfortunately finding the 20th is still out of reasonable reach for Wren. If we let this run until 15 digit numbers have been examined (the most that 53 bit integer math can accurately manage), then the time taken rises to 19 seconds - roughly 3 times slower than Phix.
However, we need 64 bit integer arithmetic to get up to 20 digits and this requires the use of Wren-long which (as it's written entirely in Wren, not C) needs about 7 times longer (2 minutes 16 seconds) to even reach 15 digits. Using BigInt or GMP would be even slower.
So, if the Phix example requires 48 minutes to find the 20th number, it would probably take Wren the best part of a day to do the same which is far longer than I have patience for.
Wren
<lang ecmascript>var DMAX = 7 // maxmimum digits var LIMIT = 19 // maximum number of Disariums to find
// Pre-calculated exponential and power serials var EXP = List.filled(1 + DMAX, null) var POW = List.filled(1 + DMAX, null) EXP[0] = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] EXP[1] = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] POW[0] = List.filled(11, 0) POW[1] = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9] for (i in 2..DMAX) {
EXP[i] = List.filled(11, 0) POW[i] = List.filled(11, 0)
} for (i in 1...DMAX) {
for (j in 0..9) {
EXP[i+1][j] = EXP[i][j] * 10
POW[i+1][j] = POW[i][j] * j
}
EXP[i+1][10] = EXP[i][10] * 10
POW[i+1][10] = POW[i][10] + POW[i+1][9]
}
// Digits of candidate and values of known low bits var DIGITS = List.filled(1 + DMAX, 0) // Digits form var Exp = List.filled(1 + DMAX, 0) // Number form var Pow = List.filled(1 + DMAX, 0) // Powers form
var exp var pow var min var max var start = 1 var final = DMAX var count = 0 for (digit in start..final) {
System.print("# of digits: %(digit)")
var level = 1
DIGITS[0] = 0
while (true) {
// Check limits derived from already known low bit values
// to find the most possible candidates
while (0 < level && level < digit) {
// Reset path to try next if checking in level is done
if (DIGITS[level] > 9) {
DIGITS[level] = 0
level = level - 1
DIGITS[level] = DIGITS[level] + 1
continue
}
// Update known low bit values
Exp[level] = Exp[level - 1] + EXP[level][DIGITS[level]]
Pow[level] = Pow[level - 1] + POW[digit + 1 - level][DIGITS[level]]
// Max possible value
pow = Pow[level] + POW[digit - level][10]
if (pow < EXP[digit][1]) { // Try next since upper limit is invalidly low
DIGITS[level] = DIGITS[level] + 1
continue
}
max = pow % EXP[level][10]
pow = pow - max
if (max < Exp[level]) pow = pow - EXP[level][10]
max = pow + Exp[level]
if (max < EXP[digit][1]) { // Try next since upper limit is invalidly low
DIGITS[level] = DIGITS[level] + 1
continue
}
// Min possible value
exp = Exp[level] + EXP[digit][1]
pow = Pow[level] + 1
if (exp > max || max < pow) { // Try next since upper limit is invalidly low
DIGITS[level] = DIGITS[level] + 1
continue
}
if (pow > exp ) {
min = pow % EXP[level][10]
pow = pow - min
if (min > Exp[level]) {
pow = pow + EXP[level][10]
}
min = pow + Exp[level]
} else {
min = exp
}
// Check limits existence
if (max < min) {
DIGITS[level] = DIGITS[level] + 1 // Try next number since current limits invalid
} else {
level= level + 1 // Go for further level checking since limits available
}
}
// All checking is done, escape from the main check loop
if (level < 1) break
// Finally check last bit of the most possible candidates
// Update known low bit values
Exp[level] = Exp[level - 1] + EXP[level][DIGITS[level]]
Pow[level] = Pow[level - 1] + POW[digit + 1 - level][DIGITS[level]]
// Loop to check all last bits of candidates
while (DIGITS[level] < 10) {
// Print out new Disarium number
if (Exp[level] == Pow[level]) {
var s = ""
for (i in DMAX...0) s = s + DIGITS[i].toString
System.print(Num.fromString(s))
count = count + 1
if (count == LIMIT) {
System.print("\nFound the first %(LIMIT) Disarium numbers.")
return
}
}
// Go to followed last bit candidate
DIGITS[level] = DIGITS[level] + 1
Exp[level] = Exp[level] + EXP[level][1]
Pow[level] = Pow[level] + 1
}
// Reset to try next path
DIGITS[level] = 0
level = level - 1
DIGITS[level] = DIGITS[level] + 1
}
System.print()
}</lang>
- Output:
# of digits: 1 0 1 2 3 4 5 6 7 8 9 # of digits: 2 89 # of digits: 3 135 175 518 598 # of digits: 4 1306 1676 2427 # of digits: 5 # of digits: 6 # of digits: 7 2646798 Found the first 19 Disarium numbers. real 0m0.012s user 0m0.008s sys 0m0.004s