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 A387048 #13 Aug 18 2025 00:50:33 %S A387048 6,10,12,14,21,22,39,40,44,46,51,54,57,62,65,69,74,80,82,86,90,91,95, %T A387048 104,108,111,115,119,129,134,141,155,161,164,166,172,176,187,189,202, %U A387048 210,212,217,221,226,232,244,248,252,254,265,272,274,287,292,295,297,299,300,302,305,306,328,339 %N A387048 Numbers k such that k^2 + sopfr(k)^2 is prime, where sopfr = A001414. %C A387048 Includes 2*p where p is a prime such that 5 * p^2 + 4 * p + 4 is prime. The Generalized Bunyakowsky Conjecture implies there are infinitely many of these. %H A387048 Robert Israel, <a href="/A387048/b387048.txt">Table of n, a(n) for n = 1..10000</a> %e A387048 a(3) = 12 is a term because 12^2 + sopfr(12)^2 = 144 + (2*2+3)^2 = 193 is prime. %p A387048 sopfr:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc: %p A387048 filter:= t -> isprime(t^2 + sopfr(t)^2): %p A387048 select(filter, [$1..10^3]); %t A387048 q[k_] := PrimeQ[k^2 + (Plus @@ Times @@@ FactorInteger[k])^2]; Select[Range[2, 340], q] (* _Amiram Eldar_, Aug 14 2025 *) %Y A387048 Cf. A001414, A050703, A386991, A387049. %K A387048 nonn,new %O A387048 1,1 %A A387048 _Robert Israel_, Aug 14 2025