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A131499 Primes p such that nextprime(p)=p+4 and previousprime(p)

%I A131499 #5 Jul 16 2012 16:04:41
%S A131499 37,67,79,97,127,163,223,277,307,379,397,439,457,487,499,613,673,739,
%T A131499 757,769,853,877,907,937,967,1009,1087,1213,1297,1423,1447,1549,1567,
%U A131499 1579,1597,1663,1693,1783,1867,1993,2137,2203,2293,2347,2377,2389,2437
%N A131499 Primes p such that nextprime(p)=p+4 and previousprime(p)<p-4.
%C A131499 Or a=p+1, b=p+2 and c=p+3 are composite triples: a,b,c are composite while a-1 and c+1 are not. There are no composite twins and composite singles are interprimes of twin primes. All numbers are congruent to 1 mod 6 (and not congruent to 1 mod 10). First differences divided by 6 are: 5,2,3,5,6,10,9,5,12,3,7,3,5,2,19,10,11,3,2,14,4,5,5,5,7,13,21,14,21,4,17,...
%H A131499 Harvey P. Dale, <a href="/A131499/b131499.txt">Table of n, a(n) for n = 1..1000</a>
%e A131499 a(1)=37 because nextprime(37)=41=37+4 and previousprime(37)=31<37-4,
%e A131499 a(2)=67 because nextprime(67)=71=67+4 and previousprime(67)=61<67-4.
%t A131499 p1000=Prime[Range[1000]]; c=0; Do[p=p1000[[i]]; If[p-p1000[[i-1]]>4&&p1000[[i+1]]==4+p, c++; a[c]=p],{i,2,999}]; Table[a[i],{i,c}]
%t A131499 Select[Prime[Range[400]],NextPrime[#]-#==4&&#-NextPrime[#,-1]>4&] (* _Harvey P. Dale_, Jul 16 2012 *)
%K A131499 nonn
%O A131499 1,1
%A A131499 _Zak Seidov_, Aug 12 2007