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 A357517 #18 Nov 23 2022 08:56:50
%S A357517 5,19,270271,5105101,103515091681,3810649312471,155835500831011,
%T A357517 313986271960080721,282899575838889614011647241,
%U A357517 113405858671385228324474555982803921209616373612841704311161,2900763693484834576932132901212043025388720793126978148639249341
%N A357517 Primes that are the average of two consecutive primorial numbers A002110 plus one.
%C A357517 a(n) ends with digit 1, for n > 2.
%e A357517 19 is a term since primorials A002110(2) = 6 and A002110(3) = 30 which give (6 + 30)/2 + 1 = 19 which is prime.
%t A357517 primorial[n_] := Times@@Table[Prime[k], {k, 1, n}]; Table[If[PrimeQ[(primorial[n] + primorial[n+1])/2 + 1], (primorial[n] + primorial[n+1])/2 + 1, Nothing], {n, 1, 40}]
%Y A357517 Cf. A002110, A276939.
%K A357517 nonn
%O A357517 1,1
%A A357517 _Nicholas Leonard_, Oct 01 2022