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A269520
Primes 8k + 7 preceding the maximal gaps in A269519.
3
7, 47, 271, 311, 503, 6367, 37223, 42487, 66463, 183527, 259271, 307919, 471007, 1070567, 1801223, 5903687, 6885743, 16936247, 22413319, 38820263, 63977327, 84164447, 147452759, 150334567, 239422639, 300412031, 387154951, 473153959, 539526191, 760400783, 788128039
OFFSET
1,1
COMMENTS
Subsequence of A007522.
A269519 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 + 7 are 7 and 23, so a(1)=7. The next primes of this form are 31, 47; the gaps 31-23 and 47-31 are not records so nothing is added to the sequence. The next prime of this form is 71 and the gap 71-47=24 is a new record, so a(2)=47.
PROG
(PARI) re=0; s=7; forprime(p=23, 1e8, if(p%8!=7, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexei Kourbatov, Feb 28 2016
STATUS
approved