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