This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051642 #13 Oct 11 2021 12:10:03 %S A051642 3,5,11,19,29,101,349,521,569,571,661,1091,1489,2269,2341,2549,2659, %T A051642 2729,2731,4049,5279,6359,6871,7559,8231,9721,11719,11779,12071,13339, %U A051642 17291,17921,17959,19429,19889,20231,20359,31541,33179,33751,38651 %N 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. %C A051642 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 %H A051642 Harvey P. Dale, <a href="/A051642/b051642.txt">Table of n, a(n) for n = 0..1000</a> %t A051642 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 *) %K A051642 nonn,easy %O A051642 0,1 %A A051642 Stuart M. Ellerstein (ellerstein(AT)aol.com) %E A051642 More terms from _Joshua Zucker_, May 11 2006