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A078853 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=[6,2,4]; short d-string notation of pattern = [624].

%I A078853 #27 May 06 2017 10:07:40
%S A078853 1601,3911,5471,8081,12101,12911,13751,14621,17021,32051,38321,40841,
%T A078853 43391,58901,65831,67421,67751,68891,69821,72161,80141,89591,90011,
%U A078853 90191,97571,100511,102191,111821,112241,122021,125921,129281,129581
%N A078853 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=[6,2,4]; short d-string notation of pattern = [624].
%C A078853 All terms are == 11 (mod 30). Is 180 the minimal first difference? - _Zak Seidov_, Jun 27 2015
%C A078853 Subsequence of A049438. - _R. J. Mathar_, May 06 2017
%H A078853 R. J. Mathar, <a href="/A078853/b078853.txt">Table of n, a(n) for n = 1..1000</a>
%F A078853 Primes p = p(i) such that p(i+1)=p+6, p(i+2)=p+6+2, p(i+3)=p+6+2+4.
%e A078853 p=1601, 1601+6=1607, 1601+6+2=1609, 1601+6+2+4=1613 are consecutive primes.
%t A078853 Transpose[Select[Partition[Prime[Range[13000]], 4, 1], Differences[#]=={6, 2, 4} &]][[1]] (* _Vincenzo Librandi_, Jun 27 2015 *)
%Y A078853 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], this sequence[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].
%K A078853 nonn
%O A078853 1,1
%A A078853 _Labos Elemer_, Dec 11 2002
%E A078853 Listed terms verified by _Ray Chandler_, Apr 20 2009