A268929 Primes 6k - 1 preceding the maximal gaps in A268928.

5, 29, 113, 197, 521, 1109, 1733, 6389, 7349, 35603, 148517, 180797, 402593, 406907, 2339039, 5521721, 11157989, 20831267, 22440701, 27681263, 73451723, 241563407, 953758109, 1444257671, 1917281213, 6822753629, 15867286361, 28265029631, 40841579819, 177858259463

Offset

1,1

Comments

Subsequence of A007528 and A334544.

A268928 lists the corresponding record gap sizes. See more comments there.

Links

Alexei Kourbatov, Table of n, a(n) for n = 1..37

Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Formula

a(n) = A268930(n) - A268928(n). - Alexei Kourbatov, Jun 15 2020.

Example

The first two primes of the form 6k-1 are 5 and 11, so a(1)=5. The next primes of this form are 17, 23, 29; the gaps 17-11 = 23-17 = 29-23 are not records so nothing is added to the sequence. The next prime of this form is 41 and the gap 41-29=12 is a new record, so a(2)=29.

Prog

(PARI) re=0; s=5; forprime(p=11, 1e8, if(p%6!=5, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)

Crossrefs

Cf. A007528, A268928, A268930, A334543, A334544.

Sequence in context: A085151 A119494 A334544 * A268244 A297632 A153077

Adjacent sequences: A268926 A268927 A268928 * A268930 A268931 A268932

Keyword

nonn

Author

Alexei Kourbatov, Feb 15 2016

Status

approved