A078857 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].

47, 167, 257, 557, 587, 647, 1217, 2957, 4007, 6257, 6857, 7577, 10847, 11927, 14537, 16217, 17477, 19457, 24407, 25457, 26687, 26717, 29867, 41507, 41597, 48527, 51407, 54617, 56087, 60077, 61547, 68477, 75527, 82457, 84047, 94427, 101267

Offset

1,1

Comments

Subsequence of A047948. - R. J. Mathar, Feb 11 2013

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Formula

Primes p = p(i) such that p(i+1)=p+6, p(i+2)=p+6+6, p(i+3)=p+6+6+2.

Example

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

Mathematica

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

Crossrefs

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].

Sequence in context: A141994 A185938 A132251 * A216827 A139992 A142916

Adjacent sequences: A078854 A078855 A078856 * A078858 A078859 A078860

Keyword

nonn

Author

Labos Elemer, Dec 11 2002

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Status

approved