A268801 Primes 4k + 3 at the end of the maximal gaps in A268799.

7, 19, 43, 103, 307, 419, 1367, 2647, 7411, 7823, 11239, 11699, 31511, 47051, 148063, 288179, 360779, 425779, 507347, 666403, 1414943, 2199143, 3358423, 9287939, 11512843, 11648887, 24315443, 42454267, 145555231, 161720627, 184008203, 766669427

Offset

1,1

Comments

Subsequence of A002145.

A268799 lists the corresponding record gap sizes. See more comments there.

Links

Alexei Kourbatov, Table of n, a(n) for n = 1..41

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)=7. 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)=19.

Prog

(PARI) re=0; s=3; forprime(p=7, 1e8, if(p%4!=3, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)

Crossrefs

Cf. A002145, A084161, A268799, A268800.

Sequence in context: A247905 A048488 A155303 * A155275 A155268 A124700

Adjacent sequences: A268798 A268799 A268800 * A268802 A268803 A268804

Keyword

nonn

Author

Alexei Kourbatov, Feb 13 2016

Status

approved