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

0,1

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

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 *)

Crossrefs

Sequence in context: A023233 A048161 A284034 * A007671 A259589 A090471

Adjacent sequences: A051639 A051640 A051641 * A051643 A051644 A051645

Keyword

nonn,easy

Author

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

Extensions

More terms from Joshua Zucker, May 11 2006

Status

approved