Pell numbers: Difference between revisions
Added Algol W
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[211929657785303, 211929657785304, 299713796309065]
[1235216565974040, 1235216565974041, 1746860020068409]
</pre>
=={{header|ALGOL W}}==
{{Trans|FreeBASIC|via Algol 68 - basic task only and only 5 Pell primes as Algol W limits integers to 32-bit.}}
<syntaxhighlight lang="algolw">
begin % find some Pell numbers - trans FreeBasic ( which is trans Phix ) %
% returns true if n is prime, false otherwise, uses trial division %
logical procedure isPrime ( integer value n ) ;
if n < 3 then n = 2
else if n rem 3 = 0 then n = 3
else if not odd( n ) then false
else begin
logical prime;
integer f, f2, toNext;
prime := true;
f := 5;
f2 := 25;
toNext := 24; % note: ( 2n + 1 )^2 - ( 2n - 1 )^2 = 8n %
while f2 <= n and prime do begin
prime := n rem f not = 0;
f := f + 2;
f2 := toNext;
toNext := toNext + 8
end while_f2_le_n_and_prime ;
prime
end isPrime ;
integer MAX_P;
MAX_P := 9;
begin
integer array p, pl ( 0 :: 20 ); % need more than 10 Pell numbers %
integer c, pdx; % to find the fifth Pell prime %
p( 0 ) := 0; p( 1 ) := 1;
pl( 0 ) := 2; pl( 1 ) := 2;
for n := 2 until 20 do begin
p( n ) := 2 * p( n - 1 ) + p( n - 2 );
pl( n ) := 2 * pl( n - 1 ) + pl( n - 2 )
end for_n ;
write( "First 10 Pell numbers:" );
for n := 0 until MAX_P do begin writeon( i_w := 1, s_w := 0, " ", p( n ) ) end;
write();write( "First 10 Pell-Lucas numbers:" );
for n := 0 until MAX_P do begin
writeon( i_w := 1, s_w := 0, " ", pl( n ) )
end for_n ;
write( s_w := 0, "First 10 rational approximations of sqrt(2) (" );
writeon( s_w := 0, r_format := "A", r_w := 8, r_d := 6, sqrt( 2 ), "):" );
for n := 1 until MAX_P do begin
integer j;
j := pl( n ) div 2;
write( i_w := 1, s_w := 0, " ", j, "/", p( n ), " ~= "
, r_format := "A", r_w := 8, r_d := 6, j / p( n )
)
end for_n;
write();write( "First 5 Pell primes:" ); write( "index Pell prime" );
c := 0;
pdx := 2;
while c < 5 do begin
if isPrime( p( pdx ) ) then begin
write( i_w := 5, s_w := 0, pdx, " ", i_w := 1, p( pdx ) );
c := c + 1
end if_isPrime_p_pdx ;
pdx := pdx + 1
end while_c_lt_5 ;
write(); write( "First 10 Newman-Shank-Williams numbers:" );write();
for n := 0 until MAX_P do begin
integer nsw;
nsw := p( 2 * n ) + p( 2 * n + 1 );
writeon( i_w := 1, s_w := 0, " ", nsw )
end for_n;
write();write( "First 10 near isosceles right triangles:" );
begin
integer i, i0, i1, i2, t, found;
i0 := 0; i1 := 1; t := 1; found := 0;
i := 1;
while found < 10 do begin
i := i + 1;
i2 := i1*2 + i0;
if odd( i ) then begin
write( i_w := 1, s_w := 0, " [", t, ", ", t + 1, ", ", i2, "]" );
found := found + 1
end if_odd_i ;
t := t + i2; i0 := i1; i1 := i2
end while_found_lt_10
end
end
end.
</syntaxhighlight>
{{out}}
<pre style="height:40ex;overflow:scroll;">
First 10 Pell numbers: 0 1 2 5 12 29 70 169 408 985
First 10 Pell-Lucas numbers: 2 2 6 14 34 82 198 478 1154 2786
First 10 rational approximations of sqrt(2) (1.414213):
1/1 ~= 1.000000
3/2 ~= 1.500000
7/5 ~= 1.400000
17/12 ~= 1.416666
41/29 ~= 1.413793
99/70 ~= 1.414285
239/169 ~= 1.414201
577/408 ~= 1.414215
1393/985 ~= 1.414213
First 5 Pell primes:
index Pell prime
2 2
3 5
5 29
11 5741
13 33461
First 10 Newman-Shank-Williams numbers:
1 7 41 239 1393 8119 47321 275807 1607521 9369319
First 10 near isosceles right triangles:
[2, 3, 5]
[12, 13, 29]
[70, 71, 169]
[408, 409, 985]
[2378, 2379, 5741]
[13860, 13861, 33461]
[80782, 80783, 195025]
[470832, 470833, 1136689]
[2744210, 2744211, 6625109]
[15994428, 15994429, 38613965]
</pre>
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