

A330855


Primes 6k + 1 at the end of firstoccurrence 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
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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 1913=6 already occurred, so a new term is not added to the sequence. The next prime 6k+1 is 31, and the gap 3119=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=ps; if(isFirstOcc[g/6], print1(p", "); isFirstOcc[g/6]=0); s=p)


CROSSREFS

Cf. A002476, A014320, A058320, A268927, A330853 (firstoccurrence gap sizes), A330854 (primes beginning the firstoccurrence 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



