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 A292743 #8 Oct 07 2017 22:39:43
%S A292743 6353,14731,19463,71333,77543,78781,83417,104701,105557,130651,185021,
%T A292743 202799,214433,218111,344243,351031,357661,358429,380417,408203,
%U A292743 443221,466547,496471,505091,587117,593491,634241,652733,702497,746177,778241,807011,886973,949951
%N A292743 Initial member of 6 consecutive primes a, b, c, d, e, f such that (a + f) = (b + e), (a + e) = (b + d) and (c + f) = (d + e).
%C A292743 None of the terms <= 10^7, is the smaller of twin primes.
%C A292743 78781 is the first term that is greater of twin primes; 78781 - 2 = 78779 is prime.
%e A292743 6353 is a term because it is the initial member of 6 consecutive primes {6353, 6359, 6361, 6367, 6373, 6379} = {a, b, c, d, e, f}; and (a + f) = (b + e), (a + e) = (b + d) and (c + f) = (d + e).
%p A292743 A292743:= proc(n)local a,b,c,d,e,f; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2); d:=ithprime(n+3); e:=ithprime(n+4); f:=ithprime(n+5); if (a + f) = (b + e) and (a + e) = (b + d) and (c + f) = (d + e) then RETURN (ithprime(n)); fi; end: seq(A292743(n), n=1..100000);
%t A292743 Select[Partition[Prime@ Range[10^5], 6, 1], Function[{a, b, c, d, e, f}, And[(a + f) == (b + e), (a + e) == (b + d), (c + f) == (d + e)]] @@ # &][[All, 1]] (* _Michael De Vlieger_, Sep 22 2017 *)
%Y A292743 Cf. A000040, A292618, A292715.
%K A292743 nonn
%O A292743 1,1
%A A292743 _K. D. Bajpai_, Sep 22 2017