A052376 Primes followed by a [10,2,10] prime difference pattern of A001223.

409, 1039, 2017, 2719, 3571, 4219, 4231, 4261, 4327, 6079, 6121, 6679, 6781, 8209, 11047, 11149, 11959, 12241, 15277, 19531, 19687, 21577, 21589, 26881, 27529, 28087, 28297, 29389, 30829, 30859, 31069, 32401, 42061, 45307, 47797, 48109

Offset: 1

Author

Labos Elemer, Mar 22 2000

Keywords

• nonn

Comments

Subsequence of lesser terms of 10-twins (A031928).

Start primes of quadruples consisting of two consecutive 10-twins of prime which are in minimal distance [minD = A052380(10/2) = 12].

First term of this sequence is 409 = A052381(5).

Examples

			p=1039 begins [1039,1049,1051,1061] prime quadruple with the appropriate difference pattern: [10,2,10]=[d,D-d,d], so d=10, D=12.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1780

Crossrefs

Cf. A031928, A053323, A052380, A052381, A052377, A052378.

Programs

Mathematica

{p, q, r, s} = {2, 3, 5, 7}; lst = {}; While[p < 50000, If[ Differences[{p, q, r, s}] == {10, 2, 10}, AppendTo[lst, p]]; {p, q, r, s} = {q, r, s, NextPrime@ s}]; lst (* Robert G. Wilson v, Jul 15 2015 *)

Formula

a(n)=p, a prime which begins a [p, p+d, p+D, p+D+d]=[p, p+10, p+12, p+22] prime quadruple.

a(n) = A259025(n)-11. - Robert G. Wilson v, Jul 15 2015