A056869 Prime hypotenuses of Pythagorean triangles with consecutive integer sides.

5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281

Offset

1,1

Comments

These primes belong to A001653.

From Jianing Song, Jan 02 2019: (Start)

Essentially the same sequence as A086383.

If p is a term then it is a unique-period prime in base sqrt(2*p^2 - 1). (End)

Links

Robert Israel, Table of n, a(n) for n = 1..22

Formula

a(n) = A086383(n+1). - Jianing Song, Jan 02 2019

Example

29 is included because it is prime and it is the hypotenuse of the 20, 21, 29 Pythagorean triangle.

Maple

f:= gfun:-rectoproc({a(n)=6*a(n-1)-a(n-2), a(1)=1, a(2)=5}, a(n), remember):
select(isprime, [seq(f(n), n=1..1000)]); # Robert Israel, Oct 13 2015

Mathematica

Select[Sqrt[#^2+(#+1)^2]&/@With[{p=3+2Sqrt[2]}, NestList[Floor[p #]+3&, 3, 120]], PrimeQ] (* Harvey P. Dale, May 02 2018 *)

Prog

(PARI) t(n) = if(n<3, 5^(n-1), 6*t(n-1)-t(n-2));
for(n=1, 50, if(isprime(t(n)), print1(t(n)", "))) \\ Altug Alkan, Oct 13 2015
(GAP) f:=[1, 5];; for n in [3..60] do f[n]:=6*f[n-1]-f[n-2]; od; a:=Filtered(f, IsPrime);; Print(a); # Muniru A Asiru, Jan 03 2019

Crossrefs

Cf. A000129, A001653, A001652, A046090, A086383.

Sequence in context: A237188 A371347 A086720 * A228028 A237256 A172041

Adjacent sequences: A056866 A056867 A056868 * A056870 A056871 A056872

Keyword

nonn

Author

Harvey P. Dale, Sep 02 2000

Extensions

Incorrect link to index entries for linear recurrences with constant coefficients removed by Colin Barker, Oct 13 2015

Offset changed to 1 by Colin Barker, Oct 13 2015

Status

approved