

A268926


Primes 6k + 1 preceding the maximal gaps in A268925.


4



7, 19, 43, 241, 1327, 4363, 7789, 22189, 24247, 38461, 40237, 69499, 480169, 1164607, 1207699, 1467937, 1526659, 3975721, 11962651, 14466637, 19097257, 30097861, 39895309, 198389311, 303644227, 393202123, 485949253, 680676109, 1917214927, 3868900621, 4899889741, 6957509653, 7599382573
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OFFSET

1,1


COMMENTS

Subsequence of A002476 and A330854.
A268925 lists the corresponding record gap sizes. See more comments there.


LINKS

Alexei Kourbatov, Table of n, a(n) for n = 1..36
Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.


FORMULA

a(n) = A268927(n)  A268925(n).  Alexei Kourbatov, Jun 21 2020


EXAMPLE

The first two primes of the form 6k+1 are 7 and 13, so a(1)=7. The next prime of this form is 19; the gap 1913 is not a record so nothing is added to the sequence. The next prime of this form is 31 and the gap 3119=12 is a new record, so a(2)=19.


PROG

(PARI) re=0; s=7; forprime(p=13, 1e8, if(p%6!=1, next); g=ps; if(g>re, re=g; print1(s", ")); s=p)


CROSSREFS

Cf. A002476, A268925, A268927, A330853, A330854.
Sequence in context: A113927 A155399 A330854 * A212955 A155415 A155273
Adjacent sequences: A268923 A268924 A268925 * A268927 A268928 A268929


KEYWORD

nonn


AUTHOR

Alexei Kourbatov, Feb 15 2016


STATUS

approved



