A052378 Primes followed by a [4,2,4] prime difference pattern of A001223.

7, 13, 37, 97, 103, 223, 307, 457, 853, 877, 1087, 1297, 1423, 1483, 1867, 1993, 2683, 3457, 4513, 4783, 5227, 5647, 6823, 7873, 8287, 10453, 13687, 13873, 15727, 16057, 16063, 16183, 17383, 19417, 19423, 20743, 21013, 21313, 22273, 23053, 23557

Offset: 1

Author

Labos Elemer, Mar 22 2000

Keywords

• nonn

Comments

The sequence includes A052166, A052168, A022008 and also other primes like 13, 103, 16063 etc.

a(n) is the lesser term of a 4-twin (A023200) after which the next 4-twin comes in minimal distance [here it is 2; see A052380(4/2)].

Analogous prime sequences are A047948, A052376, A052377 and A052188-A052198 with various [d, A052380(d/2), d] difference patterns following a(n).

All terms == 1 (mod 6) - Zak Seidov, Aug 27 2012

Subsequence of A022005. - R. J. Mathar, May 06 2017

Examples

			103 initiates [103,107,109,113] prime quadruple followed by [4,2,4] difference pattern.
		

Links

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

Crossrefs

Cf. A023200, A053320, A022008, A052166, A052168, A001223, A052380.

Programs

Mathematica

a = {}; Do[If[Prime[x + 3] - Prime[x] == 10, AppendTo[a, Prime[x]]], {x, 1, 10000}]; a (* Zerinvary Lajos, Apr 03 2007 *)
Select[Partition[Prime[Range[3000]],4,1],Differences[#]=={4,2,4}&][[All,1]] (* Harvey P. Dale, Jun 16 2017 *)

PARI

is(n)=n%6==1 && isprime(n+4) && isprime(n+6) && isprime(n+10) && isprime(n) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) is the initial prime of a [p, p+4, p+6, p+6+4] prime-quadruple consisting of two 4-twins: [p, p+4] and [p+6, p+10].