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 A284035 #27 Jan 29 2024 19:17:26
%S A284035 5,13,61,181,421,3121,5101,60901,83641,100801,135721,161881,163021,
%T A284035 218461,273061,491041,595141,637321,697381,1064341,1108561,1171981,
%U A284035 1806901,2574181,2601481,2740141,2763601,2853661,3248701,3535141,3567121,3696481,3723721,3729181,4832941
%N A284035 Upper twin primes which correspond to the hypotenuse in a Pythagorean triple whose short leg is also a prime.
%C A284035 A284034 gives the corresponding short leg primes in the definition.
%F A284035 A284034(n)^2 + (a(n) - 1)^2 = a(n)^2, i.e., a(n) = (A284034(n)^2 + 1)/2.
%e A284035 The prime q = 3121 is in the sequence because q - 2 = 3119 is prime and {79, 3120, 3121} is a Pythagorean triple with prime short leg (see example in A284034).
%o A284035 (PARI) lista(nn) = forprime(p=3, nn, if (isprime(p) && isprime((p^2-3)/2) && isprime(q=(p^2+1)/2), print1(q, ", "))); \\ _Michel Marcus_, Apr 01 2017
%Y A284035 Cf. A051859, A067756, A284034.
%K A284035 nonn
%O A284035 1,1
%A A284035 _Giuseppe Coppoletta_, Mar 19 2017
%E A284035 More terms from _Michel Marcus_, Apr 01 2017