A078858 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, 4]; short d-string notation of pattern = [664].

151, 367, 601, 727, 2281, 2671, 3307, 4987, 5557, 10651, 12967, 13171, 15907, 18217, 18427, 20101, 20341, 24091, 27061, 28591, 30097, 30307, 31321, 32491, 35311, 37951, 41941, 42181, 42391, 45751, 52951, 53617, 55201, 56767, 59107, 65407

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+4.

Example

p=151, 151+6 = 157, 151+6+6 = 163, 151+6+6+4 = 167 are consecutive primes.

Mathematica

Transpose[Select[Partition[Prime[Range[6600]], 4, 1], Differences[#] == {6, 6, 4}&]][[1]] (* Harvey P. Dale, Nov 04 2011 *)

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: A140022 A211551 A108842 * A217498 A078967 A089317

Adjacent sequences: A078855 A078856 A078857 * A078859 A078860 A078861

Keyword

nonn

Author

Labos Elemer, Dec 11 2002

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Status

approved