A330854 Primes of the form 6k + 1 preceding the first-occurrence gaps in A330853.

7, 19, 43, 241, 283, 1327, 1489, 1951, 2389, 4363, 7789, 10177, 16759, 22189, 24247, 38461, 40237, 43441, 69499, 75403, 100801, 118927, 171271, 195541, 204163, 250279, 480169, 577639, 590437, 1164607, 1207699, 1278817, 1382221, 1467937, 1526659, 1889803, 2314369

Offset

1,1

Comments

Subsequence of A002476. First differs from A268926 in that that sequence does not include 283; all terms of A268926 are in this sequence but many terms of this sequence are not in A268926.

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) = A330855(n) - A330853(n).

Example

The first two primes of the form 6k + 1 are 7 and 13, so a(1) = 7. The next prime of that form is 19, and the gap 19 - 13 = 6 already occurred; so a new term is not added to the sequence. The next prime of the form 6k + 1 is 31, and the gap 31 - 19 = 12 is occurring for the first time; therefore a(2) = 19.
The gap between 241 and the next prime of the form 6k + 1 (271) is 30. So 241 is in the sequence.
Although the gap between 283 and 307 is only 24 (which is less than 30), the gap is of a size not previously encountered. So 283 is in the sequence.

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(s", "); isFirstOcc[g/6]=0); s=p)

Crossrefs

Cf. A002476, A014320, A058320, A330853 (gap sizes), A330855.

Sequence in context: A155247 A113927 A155399 * A268926 A212955 A155415

Adjacent sequences: A330851 A330852 A330853 * A330855 A330856 A330857

Keyword

nonn

Author

Alexei Kourbatov, Apr 27 2020

Status

approved