A078852 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=[4, 6,6]; short d-string notation of pattern = [466].

43, 163, 643, 937, 967, 1093, 1213, 2953, 4003, 4447, 6967, 7573, 8737, 9463, 10243, 10597, 11923, 12487, 12637, 13033, 14533, 14737, 15787, 16087, 16417, 16477, 16927, 17317, 17467, 20113, 22063, 25453, 26683, 26713, 27763, 29863, 32983

Offset: 1

Author

Labos Elemer, Dec 11 2002

Keywords

• nonn

Comments

Subsequence of A078561. - R. J. Mathar, Feb 11 2013

Examples

			p=43,43+4=47,43+4+6=53,43+4+6+6=59 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

Transpose[Select[Partition[Prime[Range[4000]],4,1],Differences[#]=={4,6,6}&]][[1]] (* Harvey P. Dale, Dec 15 2015 *)

PARI

isok(n) = isprime(n) && (nextprime(n+1) == (n+4)) && (nextprime(n+5) == (n+10)) && (nextprime(n+11) == (n+16)) \\ Michel Marcus, Jul 23 2013

Formula

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

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009