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

1,1

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.

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.

Formula

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

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A065768 A155820 A242231 * A268927 A061239 A072023

Adjacent sequences: A330852 A330853 A330854 * A330856 A330857 A330858

Keyword

nonn

Author

Alexei Kourbatov, Apr 27 2020

Status

approved