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A269520 Primes 8k + 7 preceding the maximal gaps in A269519. 3


%S 7,47,271,311,503,6367,37223,42487,66463,183527,259271,307919,471007,

%T 1070567,1801223,5903687,6885743,16936247,22413319,38820263,63977327,

%U 84164447,147452759,150334567,239422639,300412031,387154951,473153959,539526191,760400783,788128039

%N Primes 8k + 7 preceding 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="/A269520/b269520.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)=7. 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)=47.

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

%Y Cf. A007522, A269519, A269521.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Feb 28 2016

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Last modified April 1 19:13 EDT 2023. Contains 361695 sequences. (Running on oeis4.)