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

Author

Alexei Kourbatov, Apr 27 2020

Keywords

• nonn

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.

Examples

			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.
		

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, A330853 (gap sizes), A330855.

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

Formula

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