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 A288632 #26 Mar 15 2024 02:24:59 %S A288632 5,7,13,19,37,67,89,109,127,307,379,389,449,487,499,683,719,769,877, %T A288632 929,937,1009,1163,1297,1523,1559,1567,1831,1933,1979,2153,2213,2221, %U A288632 2269,2389,2459,2659,2803,2857,2909,3037,3089 %N A288632 Primes p such that (p+q)/6 is prime, q is the next prime after p. %C A288632 Among first 2*10^6 primes there are 61953 terms of the sequence; e.g., a(60000)=31320053 and (31320053+31320061)/6=10440019=A000040(691876). %C A288632 Except for the case 7-5=2 the minimal value of first differences is 4. %H A288632 Zak Seidov, <a href="/A288632/b288632.txt">Table of n, a(n) for n = 1..10000</a> %e A288632 5+7=6*2, 7+11=6*3, 13+17=6*5, 19+23=6*7, 37+41=6*11, 67+71=6*23. %t A288632 Select[Prime[Range[1000]], PrimeQ[(# + NextPrime[#])/6] &] %Y A288632 Cf. A000040, A001043. %K A288632 nonn %O A288632 1,1 %A A288632 _Zak Seidov_, Jun 12 2017