A056869 Prime hypotenuses of Pythagorean triangles with consecutive integer sides.

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

Offset: 1

Author

Harvey P. Dale, Sep 02 2000

Keywords

• nonn

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)

Examples

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

Links

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

Crossrefs

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

Programs

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

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 *)

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

Formula

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

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