A330855 Primes 6k + 1 at the end of first-occurrence gaps in A330853.

13, 31, 61, 271, 307, 1381, 1531, 1987, 2437, 4423, 7867, 10243, 16831, 22273, 24337, 38557, 40351, 43543, 69661, 75511, 100927, 119047, 171403, 195691, 204301, 250423, 480343, 577807, 590593, 1164799, 1207903, 1278997, 1382419, 1468189, 1526929, 1890019, 2314591

Offset: 1

Author

Alexei Kourbatov, Apr 27 2020

Keywords

• nonn

Comments

Subsequence of A002476. Contains A268927 as a subsequence. First differs from A268927 at a(5)=307.

A330853 lists the corresponding gap sizes; see more comments there.

Examples

			The first two primes of the form 6k+1 are 7 and 13, so a(1)=13. The next prime 6k+1 is 19, and the gap 19-13=6 already occurred, so a new term is not added to the sequence. The next prime 6k+1 is 31, and the gap 31-19=12 is occurring for the first time; therefore a(2)=31.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..135
• Alexei Kourbatov and Marek Wolf, On the first occurrences of gaps between primes in a residue class, arXiv preprint arXiv:2002.02115 [math.NT], 2020.

Crossrefs

Cf. A002476, A014320, A058320, A268927, A330853 (first-occurrence gap sizes), A330854 (primes beginning the first-occurrence gaps).

Programs

PARI

isFirstOcc=vector(9999,j,1); s=7; forprime(p=13,1e8, if(p%6!=1,next); g=p-s; if(isFirstOcc[g/6], print1(p", "); isFirstOcc[g/6]=0); s=p)

Formula

a(n) = A330853(n) + A330854(n).