A268985 - OEIS

%I #11 Jan 17 2019 15:54:05

%S 11,71,331,1621,2861,4271,10891,38011,57331,137491,349471,693061,

%T 869551,1118441,1409851,3826001,5376551,7929491,11066921,13167251,

%U 13943351,18719791,31857151,51443891,68447201,104383781,149054291,180666691

%N Primes 10k + 1 preceding the maximal gaps in A268984.

%C Subsequence of A030430.

%C A268984 lists the corresponding record gap sizes. See more comments there.

%H Alexei Kourbatov, <a href="/A268985/b268985.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 10k + 1 are 11 and 31, so a(1)=11. The next primes of this form are 41, 61, 71; the gaps 41-31, 61-41, 71-61 are not records so nothing is added to the sequence. The next prime of this form is 101 and the gap 101-71=30 is a new record, so a(2)=71.

%o (PARI) re=0; s=11; forprime(p=31, 1e8, if(p%10!=1, next); g=p-s; if(g>re, re=g; print1(s", ")); s=p)

%Y Cf. A030430, A268984, A268986.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Feb 16 2016