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 A179849 #19 Sep 08 2022 08:45:54
%S A179849 19,41,53,103,151,211,229,263,313,397,419,439,461,479,523,557,571,709,
%T A179849 859,881,919,977,983,991,1033,1049,1069,1091,1103,1109,1117,1171,1187,
%U A179849 1193,1279,1301,1327,1427,1447,1453,1489,1499,1571,1621,1709,1721,1747
%N A179849 Sum of prime p and next prime after p is divisible by 7.
%C A179849 Also primes p such that the sum of p and next prime after p is a multiple of 14, since for p > 2 the sum of two consecutive primes is even. - _Klaus Brockhaus_, Jan 11 2011
%e A179849 p=19, q=23, p+q=42=7*6=14*3; p=41, q=43, p+q=84=7*12=14*6.
%t A179849 fQ[n_] := Block[{q = NextPrime@ n}, Mod[n + q, 7] == 0]; Select[ Prime@ Range@ 300, fQ]
%o A179849 (PARI) {q=3;for(n=1,100,p=q;q=nextprime(p+1);(p+q)%7==0&print(p))}
%o A179849 (Magma) IsA179849:=func< n | IsPrime(n) and (n+NextPrime(n)) mod 14 eq 0 >; [ p: p in PrimesUpTo(2000) | IsA179849(p) ]; // _Klaus Brockhaus_, Jan 11 2011
%Y A179849 Cf. A031932 (lower prime of a difference of 14 between consecutive primes), A008596 (multiples of 14).
%K A179849 nonn
%O A179849 1,1
%A A179849 _Zak Seidov_, Jan 10 2011