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A269521 Primes 8k + 7 at the end of the maximal gaps in A269519. 3

%I #11 Jan 18 2019 04:45:07

%S 23,71,311,359,599,6551,37423,42703,66751,183823,259583,308263,471391,

%T 1071023,1801727,5904247,6886367,16936991,22414079,38821039,63978127,

%U 84165271,147453599,150335431,239423519,300412927,387155903,473154943,539527199,760401839,788129191

%N Primes 8k + 7 at the end of the maximal gaps in A269519.

%C Subsequence of A007522.

%C A269519 lists the corresponding record gap sizes. See more comments there.

%H Alexei Kourbatov, <a href="/A269521/b269521.txt">Table of n, a(n) for n = 1..39</a>

%H Alexei Kourbatov and Marek Wolf, <a href="https://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

%e The first two primes of the form 8k + 7 are 7 and 23, so a(1)=23. The next primes of this form are 31, 47; the gaps 31-23 and 47-31 are not records so nothing is added to the sequence. The next prime of this form is 71 and the gap 71-47=24 is a new record, so a(2)=71.

%o (PARI) re=0; s=7; forprime(p=23, 1e8, if(p%8!=7, next); g=p-s; if(g>re, re=g; print1(p", ")); s=p)

%Y Cf. A007522, A269519, A269520.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Feb 28 2016

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Last modified October 3 22:39 EDT 2023. Contains 365872 sequences. (Running on oeis4.)