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A052165 Primes at which the difference pattern X,2,4,2,Y (X and Y >= 6) occurs in A001223.

%I A052165 #21 May 29 2018 00:51:16
%S A052165 191,821,2081,3251,9431,13001,15641,18041,18911,25301,31721,34841,
%T A052165 51341,62981,67211,69491,72221,77261,81041,82721,97841,99131,109841,
%U A052165 116531,119291,122201,135461,157271,171161,187631,194861,201491,217361
%N A052165 Primes at which the difference pattern X,2,4,2,Y (X and Y >= 6) occurs in A001223.
%C A052165 All terms == 11 (mod 30). - _Robert Israel_, Nov 30 2015
%H A052165 Robert Israel, <a href="/A052165/b052165.txt">Table of n, a(n) for n = 1..10000</a>
%e A052165 191 is here because 191 + 2 = 193, 191 + 4 + 2 = 197, 191 + 2 + 4 + 2 = 199 are primes; the prime preceding 191 is 181; the prime following 199 is 211; and the corresponding differences are 10 and 12. Thus the d-pattern "around 191" is {10,2,4,2,12}.
%p A052165 Primes:= select(isprime,[2,seq(i,i=3..10^6,2)]):
%p A052165 Gaps:= Primes[2..-1]-Primes[1..-2]:
%p A052165 Primes[select(t -> Gaps[t] = 2 and Gaps[t+1] = 4 and Gaps[t+2] = 2 and Gaps[t-1] >= 6 and Gaps[t+3]>=6, [$2..nops(Gaps)-3])]; # _Robert Israel_, Nov 30 2015
%t A052165 With[{x = 6, y = 6, s = Partition[#, 6, 1] &@ Prime@ Range[3*10^4]}, Select[s, And[First@ # >= x, Last@ # >= y, Most@ Rest@ # == {2, 4, 2}] &@ Differences@ # &]][[All, 2]] (* _Michael De Vlieger_, Oct 26 2017 *)
%Y A052165 Cf. A001223, A022008, A047078, A052160, A052162, A052163, A052164, A052167, A052168.
%K A052165 nonn
%O A052165 1,1
%A A052165 _Labos Elemer_, Jan 26 2000