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%I #18 Jul 29 2017 19:08:38
%S 23,53,263,563,593,1223,1283,1613,2333,2543,3533,4013,4643,5843,6263,
%T 6353,6563,10853,11483,14543,15263,17483,19073,19373,19463,23663,
%U 26723,29123,32363,34253,41603,48473,49193,49523,51413,51473,71333,75983
%N Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[6, 2,6]; short d-string notation of pattern = [626].
%C Subsequence of A049438. - _R. J. Mathar_, May 06 2017
%H R. J. Mathar, <a href="/A078854/b078854.txt">Table of n, a(n) for n = 1..1000</a>
%F Primes p = p(i) such that p(i+1)=p+6, p(i+2)=p+6+2, p(i+3)=p+6+2+6.
%e p=23,23+6=29,23+6+2=31,23+6+2+6=37 are consecutive primes.
%t Transpose[Select[Partition[Prime[Range[7500]],4,1],Differences[#]=={6,2,6}&]][[1]] (* _Harvey P. Dale_, Apr 17 2015 *)
%Y Cf. analogous prime quadruple sequences with various possible {2, 4, 6}-difference-patterns in brackets: A007530[242], A078847[246], A078848[264], A078849[266], A052378[424], A078850[426], A078851[462], A078852[466], A078853[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 11 2002
%E Listed terms verified by _Ray Chandler_, Apr 20 2009
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