A078848 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=[2,6,4]; short d-string notation of pattern = [264].

29, 59, 71, 269, 431, 1289, 2129, 2339, 2381, 2789, 4721, 5519, 5639, 5849, 6569, 6959, 8999, 10091, 13679, 14549, 16649, 16691, 18119, 19379, 19751, 21491, 25931, 27689, 27791, 28619, 31181, 32369, 32561, 32831, 36779, 41609, 43961, 45119

Offset

1,1

Comments

Subsequence of A049437. - R. J. Mathar, Feb 10 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+2, p(i+2)=p+2+6, p(i+3)=p+2+6+4.

Example

29, 29+2=31, 29+2+6=37, 29+2+6+4=41 are consecutive primes.

Mathematica

d = {2, 6, 4}; First /@ Select[Partition[Prime@ Range[10^4], Length@ d + 1, 1], Differences@ # == d &] (* Michael De Vlieger, May 02 2016 *)
Select[Partition[Prime[Range[4700]], 4, 1], Differences[#]=={2, 6, 4}&][[All, 1]] (* Harvey P. Dale, Mar 08 2020 *)

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: A033904 A184073 A080170 * A055784 A083821 A042666

Adjacent sequences: A078845 A078846 A078847 * A078849 A078850 A078851

Keyword

nonn

Author

Labos Elemer, Dec 11 2002

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Typo in example corrected by Michel Marcus, Dec 28 2013

Status

approved