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A078851 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=[4, 6, 2]; short d-string notation of pattern = [462].

%I A078851 #22 Jul 29 2017 19:09:44
%S A078851 19,127,229,1009,1279,1597,1609,2539,3319,3529,3907,3919,4639,4789,
%T A078851 4999,5839,5857,7477,7537,8419,9619,12097,12907,13327,15259,15877,
%U A078851 17569,17977,19069,22027,23017,24967,27739,28537,32359,33577,36919,38317
%N A078851 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=[4, 6, 2]; short d-string notation of pattern = [462].
%C A078851 Subsequence of A078561. - _R. J. Mathar_, May 06 2017
%H A078851 R. J. Mathar, <a href="/A078851/b078851.txt">Table of n, a(n) for n = 1..1000</a>
%F A078851 Primes p = p(i) such that p(i+1)=p+4, p(i+2)=p+4+6, p(i+3)=p+4+6+2.
%e A078851 p=19,19+4=23,19+4+6=29,19+4+6+2=31 are consecutive primes.
%t A078851 Select[Prime@ Range[10^4], Differences@ Prime@ Range[#, # + 3] &@ PrimePi@ # == {4, 6, 2} &] (* _Michael De Vlieger_, Jul 02 2016 *)
%Y A078851 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 A078851 nonn
%O A078851 1,1
%A A078851 _Labos Elemer_, Dec 11 2002
%E A078851 Listed terms verified by _Ray Chandler_, Apr 20 2009