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 A360155 #23 Feb 18 2023 20:50:37 %S A360155 17,59,89,131,137,233,401,449,587,617,659,683,857,971,1019,1097,1217, %T A360155 1283,1361,1481,1499,1571,1667,1787,1889,2081,2129,2411,2441,2531, %U A360155 2729,2843,2969,3137,3203,3257,3371,3491,3617,4019,4073 %N A360155 Primes of the form m^2 + 2*(k+1)^2 such that m^2 + 2*k^2 is also prime. %C A360155 Primes of the form m^2 + 2*k^2 are the norms of prime elements of Z[i*sqrt(2)]. Pairs of primes of the form (m^2 + 2*k^2, m^2 + 2*(k+1)^2) correspond to primes in Z[i*sqrt(2)] differing by i*sqrt(2). %C A360155 A prime cannot simultaneously be the lesser of such a pair and the greater of another. %F A360155 If m^2 + 2*k^2 and m^2 + 2*(k+1)^2 are primes, then m == 3 (mod 6) and k == 1 (mod 3). %e A360155 The first 3 such prime pairs are %e A360155 (11,17) = (3^2 + 2*1^2, 3^2 + 2*2^2) with m=3 and k=1, %e A360155 (41,59) = (3^2 + 2*4^2, 3^2 + 2*5^2) with m=3 and k=4, %e A360155 (83,89) = (9^2 + 2*1^2, 9^2 + 2*2^2) with m=9 and k=1. %Y A360155 See A360154 for lesser primes. %Y A360155 Cf. A000040 (prime numbers). %Y A360155 Cf. A033203 (primes of the form m^2 + 2*k^2). %K A360155 nonn %O A360155 1,1 %A A360155 _Ludovic Schwob_, Jan 28 2023