A078847 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 pattern = [2, 4, 6]; short notation = [246] d-pattern.

17, 41, 227, 347, 641, 1091, 1277, 1427, 1487, 1607, 2687, 3527, 3917, 4001, 4127, 4637, 4787, 4931, 8231, 9461, 10331, 11777, 12107, 13901, 14627, 20747, 21557, 23741, 25577, 26681, 26711, 27737, 27941, 28277, 29021, 31247, 32057, 32297

Offset

1,1

Comments

Subsequence of A022004. - R. J. Mathar, Feb 10 2013

a(n) + 12 is the greatest term in the sequence of 4 consecutive primes with 3 consecutive gaps 2, 4, 6. - Muniru A Asiru, Aug 03 2017

Links

Zak Seidov, Table of n, a(n) for n = 1..2000

Formula

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

Example

17, 17+2 = 19, 17+2+4 = 23, 17+2+4+6 = 29 are consecutive primes.

Mathematica

d = Differences[Prime[Range[10000]]]; Prime[Flatten[Position[Partition[d, 3, 1], {2, 4, 6}]]] (* T. D. Noe, May 23 2011 *)
Transpose[Select[Partition[Prime[Range[10000]], 4, 1], Differences[#] == {2, 4, 6}&]][[1]] (* Harvey P. Dale, Aug 07 2013 *)

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].

Cf. A190814[2,4,6,8], A190817[2,4,6,8,10], A190819[2,4,6,8,10,12], A190838[2,4,6,8,10,12,14]

Sequence in context: A165668 A269425 A164602 * A201028 A328022 A287308

Adjacent sequences: A078844 A078845 A078846 * A078848 A078849 A078850

Keyword

nonn

Author

Labos Elemer, Dec 11 2002

Extensions

Listed terms verified by Ray Chandler, Apr 20 2009

Additional cross references from Harvey P. Dale, May 10 2014

Status

approved