A051859 Values of C (the hypotenuse) of a Pythagorean triangle with A (the short leg) and C both prime and part of a twin prime.

5, 13, 61, 181, 421, 5101, 60901, 135721, 161881, 163021, 218461, 595141, 1108561, 2574181, 2740141, 3248701, 3535141, 3723721, 3729181, 8197201, 13933921, 20218441, 23605321, 28569241, 33874681, 47248921, 68667481, 69372421

Offset: 1

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com), Dec 14 1999

Keywords

• nonn

Comments

All terms of the sequence must be part of a Pythagorean triple of the form (2u-1), 2u*(u-1), (2u^2 - 2u + 1). - Joshua Zucker, May 12 2006

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

See A051642 for the A's and A051858 for the B's.

Subset of A067756.

Programs

Mathematica

tppQ[{a_,b_,c_}]:=AllTrue[{a,c},PrimeQ]&&AnyTrue[a+{2,-2},PrimeQ] && AnyTrue[ c+{2,-2},PrimeQ]; Select[Table[{2n-1,2n(n-1),2n^2-2n+1},{n,2,10000}],tppQ][[All,3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 27 2021 *)

Formula

A051858 + 1, or 2*A051891^2 - 2*A051891 + 1, or 2*A051892^2 + 2*A051892 + 1. - Joshua Zucker, May 12 2006

Extensions

More terms from Joshua Zucker, May 12 2006