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%I A258578 #10 Jun 20 2019 13:23:41
%S A258578 23,31,47,53,61,73,83,131,151,157,167,173,199,211,233,251,257,263,271,
%T A258578 331,353,367,373,383,433,443,467,503,509,523,541,557,563,571,587,593,
%U A258578 601,607,619,647,653,661,677,727,733,751,797,941,947,971,977,991,997
%N A258578 Primes p such that difference between p and next prime after p is multiple of 6.
%C A258578 A031924 is subsequence: first 12 terms are the same.
%H A258578 Charles R Greathouse IV, <a href="/A258578/b258578.txt">Table of n, a(n) for n = 1..10000</a>
%e A258578 a(1)=23 because next prime after 23 is 29=23+6,
%e A258578 a(13)=199 because next prime after 199 is 211=199+12,
%e A258578 a(30)=523 because next prime after 523 is 541=523+18,
%e A258578 a(90)=1669 because next term after 1669 is 1693=1669+24,
%e A258578 a(199)=4297 because next prime after 4297 is 4327=4297+30.
%t A258578 Select[Partition[Prime[Range[200]],2,1],Mod[#[[2]]-#[[1]],6]==0&][[All,1]] (* _Harvey P. Dale_, Jun 20 2019 *)
%o A258578 (PARI) lista(nn) = forprime(p=2, nn, if (!((nextprime(p+1) - p) % 6), print1(p, ", "));); \\ _Michel Marcus_, Jun 04 2015
%o A258578 (PARI) v=List();p=2; forprime(q=3,1e4,if((q-p)%6==0,listput(v,p));p=q); v \\ _Charles R Greathouse IV_, Jun 04 2015
%Y A258578 Cf. A031924, A124582, A130796.
%K A258578 nonn
%O A258578 1,1
%A A258578 _Zak Seidov_, Jun 04 2015

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