A078856 Initial term in sequence of four consecutive primes whose consecutive differences have d-pattern = [6, 4, 6]; short d-string notation for pattern = [646].

73, 157, 373, 433, 1543, 2341, 2383, 3313, 3607, 4441, 4993, 5851, 6037, 6961, 7237, 8731, 9613, 9733, 10723, 13093, 14143, 14731, 16411, 16921, 17971, 18787, 20107, 21391, 23011, 23593, 25111, 25237, 25447, 27793, 30103, 30697, 32353, 32563

Offset: 1

Author

Labos Elemer, Dec 11 2002

Keywords

• nonn

Examples

			p=73, 73 + 6 = 79, 73 + 6 + 4 = 83, 73 + 6 + 4 + 6 = 89 are consecutive primes.
		

Links

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

Crossrefs

Subsequence of A078562.

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

Maple

N:=10^4: # to get all terms <= N.
Primes:=select(isprime,[seq(i,i=3..N+16,2)]):
Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1],
Primes[t+3]-Primes[t+2]]=[6,4,6], [$1..nops(Primes)-3])]; # Muniru A Asiru, Aug 04 2017

Mathematica

Transpose[Select[Partition[Prime[Range[10000]],4,1],Differences[#]=={6,4,6}&]][[1]] (* Harvey P. Dale, Apr 22 2014 *)

Formula

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

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Name simplified by Michel Marcus, Aug 11 2017