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A268800
Primes 4k + 3 preceding the maximal gaps in A268799.
3
3, 11, 31, 83, 283, 383, 1327, 2591, 7351, 7759, 11171, 11587, 31391, 46919, 147919, 288023, 360611, 425603, 507163, 666203, 1414703, 2198887, 3358151, 9287659, 11512547, 11648531, 24315047, 42453823, 145554779, 161720147, 184007671, 766668811
OFFSET
1,1
COMMENTS
Subsequence of A002145.
A268799 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 4k+3 are 3 and 7, so a(1)=3. The next prime of this form is 11; the gap 11-7 is not a record so no term is added to the sequence. The next prime of this form is 19; the gap 19-11=8 is a new record so a(2)=11.
PROG
(PARI) re=0; s=3; forprime(p=7, 1e8, if(p%4!=3, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexei Kourbatov, Feb 13 2016
STATUS
approved