login
A269421
Primes 8k + 3 preceding the maximal gaps in A269420.
2
3, 19, 179, 379, 691, 1187, 1307, 4787, 15467, 22307, 43067, 83579, 273323, 373459, 1543291, 5364091, 5768803, 20941259, 137649667, 251522291, 369352163, 426008699, 938378747, 1042908091, 1378014731, 1878780427, 11474650339, 12402606331, 15931938899, 51025309339, 144309631099
OFFSET
1,1
COMMENTS
Subsequence of A007520.
A269420 lists the corresponding record gap sizes. See more comments there.
LINKS
Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
EXAMPLE
The first two primes of the form 8k + 3 are 3 and 11, so a(1)=3. The next prime of this form is 19; the gap 19-11 is not a record so nothing is added to the sequence. The next prime of this form is 43 and the gap 43-19=24 is a new record, so a(2)=19.
PROG
(PARI) re=0; s=3; forprime(p=11, 1e8, if(p%8!=3, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexei Kourbatov, Feb 25 2016
STATUS
approved