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 A258153 #8 Jul 24 2021 18:34:34
%S A258153 6,7,9,11,15,17,21,23,27,28,30,32,33,35,36,38,41,42,44,45,47,48,51,52,
%T A258153 54,56,57,60,62,63,65,66,68,71,72,75,77,78,80,83,84,86,87,90,92,93,96,
%U A258153 98,101,102,104,105,107,108,110,111,113,114,116,117,120,122,126,128,131,132,134,135,138,141
%N A258153 Numbers of the form p^2 + q with p, q and 2*p + 3 all prime.
%C A258153 The conjecture in A258141 asserts that any six consecutive positive integers contain at least a term of the current sequence.
%H A258153 Zhi-Wei Sun, <a href="/A258153/b258153.txt">Table of n, a(n) for n = 1..10000</a>
%e A258153 a(1) = 6 since 6 = 2^2 + 2 with 2 and 2*2+3 = 7 both prime.
%e A258153 a(2) = 7 since 7 = 2^2 + 3 with 2, 3, 2*2+3 all prime.
%t A258153 n=0;Do[Do[If[PrimeQ[2Prime[k]+3]&&PrimeQ[m-Prime[k]^2],n=n+1;Print[n," ",m];Goto[aa]],{k,1,PrimePi[Sqrt[m]]}];
%t A258153 Label[aa];Continue,{m,1,141}]
%t A258153 Module[{pp=40},Select[Union[#[[1]]^2+#[[2]]&/@Select[Tuples[ Prime[ Range[ pp]],2],PrimeQ[2#[[1]]+3]&]],#<=Prime[pp]-4&]] (* _Harvey P. Dale_, Jul 24 2021 *)
%Y A258153 Cf. A000040, A023204, A258139, A258140, A258141.
%K A258153 nonn
%O A258153 1,1
%A A258153 _Zhi-Wei Sun_, May 22 2015