A268800 Primes 4k + 3 preceding the maximal gaps in A268799.

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, 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)=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

Cf. A002145, A084161, A268799, A268801.

Sequence in context: A087323 A236752 A034543 * A054343 A369442 A320238

Adjacent sequences: A268797 A268798 A268799 * A268801 A268802 A268803

Keyword

nonn

Author

Alexei Kourbatov, Feb 13 2016

Status

approved