A078855 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, 4,2]; short d-string notation of pattern = [642].

31, 61, 271, 607, 1291, 1657, 1777, 1861, 1987, 2131, 2371, 2677, 2791, 4507, 5407, 5431, 5641, 7867, 9001, 11821, 13681, 14551, 17377, 18121, 18301, 20347, 21481, 22147, 24097, 27271, 32707, 35521, 36781, 37561, 41221, 41947, 42397, 42451

Offset

1,1

Comments

Subsequence of A078562. - R. J. Mathar, May 06 2017

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+4, p(i+3)=p+6+4+2.

Example

p=31,31+6=37,31+6+4=41,31+6+4+2=43 are consecutive primes.

Mathematica

Transpose[Select[Partition[Prime[Range[4500]], 4, 1], Differences[#] == {6, 4, 2}&]][[1]] (* Harvey P. Dale, Feb 10 2015 *)

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: A088464 A088463 A195745 * A053430 A040930 A115809

Adjacent sequences: A078852 A078853 A078854 * A078856 A078857 A078858

Keyword

nonn

Author

Labos Elemer, Dec 11 2002

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Status

approved