A078955 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,2,6).

19, 1279, 1609, 2539, 3529, 4639, 5839, 15259, 19069, 32359, 71329, 75979, 88789, 97369, 112909, 113149, 130639, 135589, 138559, 191449, 229759, 246919, 290659, 312199, 346429, 349369, 357649, 384469, 396619, 416389, 418339, 421699, 433249, 435559, 450799, 460969

Offset

1,1

Comments

Equivalently, primes p such that p, p+4, p+10, p+12 and p+18 are consecutive primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) == 19 (mod 30). - Amiram Eldar, Feb 21 2025

Example

19 is in the sequence since 19, 23 = 19 + 4, 29 = 19 + 10, 31 = 19 + 12 and 37 = 19 + 18 are consecutive primes.

Mathematica

Transpose[Select[Partition[Prime[Range[40000]], 5, 1], Differences[#]=={4, 6, 2, 6}&]][[1]]  (* Harvey P. Dale, Feb 03 2011 *)

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 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 21 2025

Crossrefs

Subsequence of A078851. - R. J. Mathar, May 06 2017

Cf. A001223, A078866, A078867, A078946-A078969, A022006, A022007.

Sequence in context: A316332 A319025 A253127 * A383167 A107673 A130037

Adjacent sequences: A078952 A078953 A078954 * A078956 A078957 A078958

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved