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

1,1

Links

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

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.

Example

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

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 *)

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].

Sequence in context: A044705 A248399 A071844 * A142326 A142377 A044405

Adjacent sequences: A078853 A078854 A078855 * A078857 A078858 A078859

Keyword

nonn

Author

Labos Elemer, Dec 11 2002

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Name simplified by Michel Marcus, Aug 11 2017

Status

approved