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A330855 Primes 6k + 1 at the end of first-occurrence gaps in A330853. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)