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%I #16 Jul 29 2017 19:08:23
%S 31,61,271,607,1291,1657,1777,1861,1987,2131,2371,2677,2791,4507,5407,
%T 5431,5641,7867,9001,11821,13681,14551,17377,18121,18301,20347,21481,
%U 22147,24097,27271,32707,35521,36781,37561,41221,41947,42397,42451
%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, 4,2]; short d-string notation of pattern = [642].
%C Subsequence of A078562. - _R. J. Mathar_, May 06 2017
%H R. J. Mathar, <a href="/A078855/b078855.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+4, p(i+3)=p+6+4+2.
%e p=31,31+6=37,31+6+4=41,31+6+4+2=43 are consecutive primes.
%t Transpose[Select[Partition[Prime[Range[4500]],4,1],Differences[#] == {6,4,2}&]][[1]] (* _Harvey P. Dale_, Feb 10 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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