A078962 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,2,6).

61, 2371, 5431, 11821, 21481, 37561, 50581, 69991, 124291, 126481, 139291, 223831, 230761, 268771, 272341, 275911, 305401, 363361, 365461, 388471, 498391, 516151, 556261, 561091, 585031, 752281, 776551, 783781, 812341, 832621, 911161, 942031, 950221, 1030021, 1108561

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, 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) == 1 (mod 30). - Amiram Eldar, Feb 22 2025

Example

61 is in the sequence since 61, 67 = 61 + 6, 71 = 61 + 10, 73 = 61 + 12 and 79 = 61 + 18 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6, 4, 2, 6} &][[;; , 1]] (* Amiram Eldar, Feb 22 2025 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 4 && p4 - p3 == 2 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A078855. - R. J. Mathar, May 06 2017

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

Sequence in context: A009841 A038650 A224441 * A000508 A191092 A234028

Adjacent sequences: A078959 A078960 A078961 * A078963 A078964 A078965

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved