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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, 6,2]; short d-string notation of pattern = [662].
18

%I #16 Jul 29 2017 19:07:54

%S 47,167,257,557,587,647,1217,2957,4007,6257,6857,7577,10847,11927,

%T 14537,16217,17477,19457,24407,25457,26687,26717,29867,41507,41597,

%U 48527,51407,54617,56087,60077,61547,68477,75527,82457,84047,94427,101267

%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, 6,2]; short d-string notation of pattern = [662].

%C Subsequence of A047948. - _R. J. Mathar_, Feb 11 2013

%H R. J. Mathar, <a href="/A078857/b078857.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+6, p(i+3)=p+6+6+2.

%e p=47,47+6=53,47+6+6=59,47+6+6+2=61 are consecutive primes.

%t Select[Partition[Prime[Range[10000]],4,1],Differences[#]=={6,6,2}&][[All,1]] (* _Harvey P. Dale_, Apr 29 2017 *)

%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