A226657 Smallest of the first four consecutive primes that comprise two sets of primes with difference 2*n.

5, 7, 23, 389, 409, 1511, 5309, 3373, 7351, 37223, 19867, 18593, 142811, 14563, 13933, 763271, 276637, 174491, 363989, 383179, 180907, 687179, 8066923, 913589, 458069, 6358777, 2507093, 5650871, 9182389, 5256071, 10237391, 9955009, 4091393, 24374033

Offset: 1

Author

Arkadiusz Wesolowski, Jun 14 2013

Keywords

• nonn

Comments

An equivalent definition of this sequence: smallest prime which gives a cluster of primes with the spacing pattern 2*n; x; 2*n, x > 0.

A229021 gives the record values. - Arkadiusz Wesolowski, Sep 11 2013

Examples

			Difference two - primes: 5, 7, 11, 13.
Difference four - primes: 7, 11, 13, 17.
Difference six - primes: 23, 29, 31, 37.
		

Links

• Index entries for primes, gaps between

Crossrefs

Cf. A000230, A133429, A133430, A229021, A229028, A229030, A229033, A229034.

Programs

Mathematica

lst = {}; Do[a = 3; While[True, b = NextPrime[a]; If[b - a == n && NextPrime[b, 2] - NextPrime[b] == n, AppendTo[lst, a]; Break[]]; a = b], {n, 2, 68, 2}]; lst
Table[SelectFirst[Partition[Prime[Range[16*10^5]],4,1],AllTrue[{#[[2]]-#[[1]],#[[4]]- #[[3]]}, EvenQ]&&#[[2]]-#[[1]]==#[[4]]-#[[3]]==2n&],{n,35}][[All,1]] (* Harvey P. Dale, Jun 07 2022 *)