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 A257553 #43 Feb 01 2024 06:09:20 %S A257553 2,3,7,17,41,239,577,665857,9369319,63018038201,489133282872437279, %T A257553 19175002942688032928599, %U A257553 123426017006182806728593424683999798008235734137469123231828679 %N A257553 Primes whose squares are not the sums of two consecutive nonsquares. %C A257553 Primes of the form A257282(k). %C A257553 2 is in this sequence, and an odd prime p is in the sequence iff either (p^2 - 1)/2 or (p^2 + 1)/2 is a square. - _Wolfdieter Lang_, May 07 2015 %C A257553 According to the Neretin comment in A257282, and as the primes of A001333 are in A086395, this is (apart from the 2) the same as A086395. - _R. J. Mathar_, Jan 31 2024 %e A257553 2 is in the sequence because it is prime and its square 4 is in A256944: 4 is not a sum of consecutive numbers. %e A257553 3 is in the sequence because it is prime and its square 9 is in A256944: 9 = 2^2 + 5. %e A257553 7 is in the sequence because it is prime and its square 49 is in A256944: 49 = 24 + 5^2. %e A257553 5 is not in the sequence because neither 12 nor 13 is a square. %t A257553 lim = 1000000; s = Plus @@@ (Partition[#, 2, 1] & @ Complement[Range@ lim, Range[Floor@ Sqrt[lim]]^2]); Select[Sqrt[#] & /@ Select[Range@ Floor[Sqrt[lim]]^2, ! MemberQ[s, #] &] , PrimeQ] (* _Michael De Vlieger_, Apr 29 2015 *) %Y A257553 Cf. A000290, A001601, A088165, A256944. %K A257553 nonn %O A257553 1,1 %A A257553 _Juri-Stepan Gerasimov_, Apr 29 2015 %E A257553 Name clarified by _Michael De Vlieger_ and _Jon E. Schoenfield_, May 03 2015 %E A257553 Edited by _Wolfdieter Lang_, May 07 2015