A078853 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=[6,2,4]; short d-string notation of pattern = [624].

1601, 3911, 5471, 8081, 12101, 12911, 13751, 14621, 17021, 32051, 38321, 40841, 43391, 58901, 65831, 67421, 67751, 68891, 69821, 72161, 80141, 89591, 90011, 90191, 97571, 100511, 102191, 111821, 112241, 122021, 125921, 129281, 129581

Offset: 1

Author

Labos Elemer, Dec 11 2002

Keywords

• nonn

Comments

All terms are == 11 (mod 30). Is 180 the minimal first difference? - Zak Seidov, Jun 27 2015

Subsequence of A049438. - R. J. Mathar, May 06 2017

Examples

			p=1601, 1601+6=1607, 1601+6+2=1609, 1601+6+2+4=1613 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], this sequence[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[13000]], 4, 1], Differences[#]=={6, 2, 4} &]][[1]] (* Vincenzo Librandi, Jun 27 2015 *)

Formula

Primes p = p(i) such that p(i+1)=p+6, p(i+2)=p+6+2, p(i+3)=p+6+2+4.

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009