A078849 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=[2, 6,6]; short d-string notation of pattern = [266].

149, 599, 3299, 4649, 5099, 6359, 11489, 12539, 16979, 19469, 27059, 30089, 31319, 34259, 42179, 53609, 58229, 63689, 65699, 71339, 75209, 77549, 78569, 80909, 81929, 85829, 87509, 87539, 89519, 92219, 101279, 105359, 112289, 116099, 116789

Offset: 1

Author

Labos Elemer, Dec 11 2002

Keywords

• nonn

Comments

Subsequence of A049437. - R. J. Mathar, Feb 10 2013

Examples

			149, 149+2=151, 149+2+6=157, 149+2+6+6=163 are consecutive primes.
		

Links

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

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].

Programs

Mathematica

d = {2, 6, 6}; First /@ Select[Partition[Prime@ Range@ 12000, Length@ d + 1, 1], Differences@ # == d &] (* Michael De Vlieger, May 02 2016 *)
Select[Partition[Prime[Range[12000]],4,1],Differences[#]=={2,6,6}&][[All,1]] (* Harvey P. Dale, Dec 29 2017 *)

Formula

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

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009