A051642 Values of A (the short leg) of a Pythagorean triangle with A and C (the hypotenuse) both prime and part of a twin prime.

3, 5, 11, 19, 29, 101, 349, 521, 569, 571, 661, 1091, 1489, 2269, 2341, 2549, 2659, 2729, 2731, 4049, 5279, 6359, 6871, 7559, 8231, 9721, 11719, 11779, 12071, 13339, 17291, 17921, 17959, 19429, 19889, 20231, 20359, 31541, 33179, 33751, 38651

Offset: 0

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com)

Keywords

• nonn
• easy

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 11 2006

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Programs

Mathematica

Select[Table[{2n-1,2n(n-1),2n^2-2n+1},{n,20000}],AllTrue[{#[[1]],#[[3]]},PrimeQ]&&AnyTrue[#[[1]]+{2,-2},PrimeQ]&&AnyTrue[#[[3]]+{2,-2},PrimeQ]&][[All,1]] (* Harvey P. Dale, Oct 11 2021 *)

Extensions

More terms from Joshua Zucker, May 11 2006