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 A240699 #22 May 26 2018 08:44:39
%S A240699 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
%T A240699 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,
%U A240699 191,193,197,199,223,227,229,233,239,241,251,257,263,269,271,277,281
%N A240699 Primes p such that at least one number among p+-2, p+-4, p+-6 is also a prime.
%C A240699 The union of A167833 and this sequence is the set of all prime numbers, A000040.
%H A240699 Lei Zhou, <a href="/A240699/b240699.txt">Table of n, a(n) for n = 1..10000</a>
%e A240699 Prime number 191: the closest prime number to 191 is 193 with 193-191 = 2 <= 6. So 191 is in this sequence.
%e A240699 Prime number 211: the closest prime number to 211 is 199 with 211-199=12 > 6. So 211 is not in this sequence.
%t A240699 p = 2; Table[While[p = NextPrime[p]; ((NextPrime[p] - p) > 6) && (6 < (p - NextPrime[p, -1]))]; p, {n, 1, 58}]
%o A240699 (PARI) forprime(p=3, 250, if(p-precprime(p-1)<7, print1(p, ", "), if(nextprime(p+1)-p<7, print1(p, ", ")))) \\ _Felix Fröhlich_, Aug 16 2014; corrected by _Michel Marcus_, May 26 2018
%Y A240699 Cf. A000040, A167833, A137870.
%K A240699 nonn,easy
%O A240699 1,1
%A A240699 _Lei Zhou_, Apr 10 2014