A078954 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,2,4).

1597, 3907, 12097, 12907, 38317, 58897, 65827, 90007, 90187, 112237, 129277, 134077, 140407, 176317, 204427, 336757, 374977, 390097, 394717, 435637, 486667, 538147, 543997, 588937, 618577, 678637, 702337, 922627, 990277, 996157, 1086247, 1248337, 1326037, 1348537

Offset

1,1

Comments

Equivalently, primes p such that p, p+4, p+10, p+12 and p+16 are consecutive primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from R. J. Mathar)

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Example

90007 is in the sequence since 90007, 90011 = 90007 + 4, 90017 = 90007 + 10, 90019 = 90007 + 12 and 90023 = 90007 + 16 are consecutive primes.

Mathematica

Transpose[Select[Partition[Prime[Range[85000]], 5, 1], Differences[#] == {4, 6, 2, 4}&]][[1]] (* Harvey P. Dale, Sep 30 2012 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 21 2025

Crossrefs

Subsequence of A078851. - R. J. Mathar, Feb 11 2013

Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Sequence in context: A179248 A068131 A068263 * A117745 A340532 A189456

Adjacent sequences: A078951 A078952 A078953 * A078955 A078956 A078957

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved