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A330854 Primes of the form 6k + 1 preceding the first-occurrence gaps in A330853. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 5 17:26 EDT 2021. Contains 343572 sequences. (Running on oeis4.)