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

Author

Alexei Kourbatov, Feb 13 2016

Keywords

• nonn

Comments

Subsequence of A002145.

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

Examples

			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.
		

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.

Crossrefs

Cf. A002145, A084161, A268799, A268800.

Programs

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)