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 A335410 #31 Jul 05 2020 12:18:57
%S A335410 11,19,73,83,227,443,883,1091,1153,1931,2593,2609,3529,4051,7451,
%T A335410 13691,15139,16649,20809,26921,34849,45377,46819,53147,56171,69193,
%U A335410 74507,74531,83233,91811,95483,103067,103969,106937,110459,112339,149059,149771,176419,180001
%N A335410 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a perfect square.
%C A335410 2*(prime(n)^2 - prime(n-1)^2) represents the integer coefficient of the difference in areas between the two circles passing through the origin with centers located at (prime(n), prime(n)) and (prime(n-1), prime(n-1)).
%C A335410 Among the first 200000 primes 2593 and 2609 are the only consecutive primes in this sequence.
%H A335410 Amiram Eldar, <a href="/A335410/b335410.txt">Table of n, a(n) for n = 1..10000</a>
%e A335410 Prime(5) = 11, prime(4) = 7, 2*(11^2 - 7^2) = 12^2, so 11 is in the sequence.
%e A335410 Prime(559) = 4051, prime(558) = 4049, 2*(4051^2 - 4049^2) = 180^2, so 4051 is in the sequence.
%t A335410 Select[Prime@ Range[2, 17000], IntegerQ@ Sqrt[2 (#^2 - NextPrime[#, -1]^2)] &] (* _Giovanni Resta_, Jun 06 2020 *)
%o A335410 (PARI) lista(nn) = {my(pp=2); forprime (p=3, nn, if (issquare(2*(p^2 - pp^2)), print1(p, ", ")); pp = p;);} \\ _Michel Marcus_, Jun 25 2020
%Y A335410 Cf. A001248, A332615.
%K A335410 nonn
%O A335410 1,1
%A A335410 _Jeff Brown_, Jun 06 2020
%E A335410 More terms from _Giovanni Resta_, Jun 06 2020