|
%I #13 Jun 02 2020 22:13:32
%S 11,41,131,227,383,557,1151,1787,4337,6449,7433,8363,9137,12893,35729,
%T 37781,58889,59879,97787,105863,130769,148667,153887,180959,220151,
%U 328271,402761,407153,416849,542441,780587,1138367,1294571,1444463,1463837,1604951
%N Primes of the form 6k - 1 at the end of first-occurrence gaps in A334543.
%C Subsequence of A007528. Contains A268930 as a subsequence. First differs from A268930 at a(5)=383.
%C A334543 lists the corresponding gap sizes; see more comments there.
%H Alexei Kourbatov, <a href="/A334545/b334545.txt">Table of n, a(n) for n = 1..160</a>
%H Alexei Kourbatov and Marek Wolf, <a href="https://arxiv.org/abs/2002.02115">On the first occurrences of gaps between primes in a residue class</a>, arXiv preprint arXiv:2002.02115 [math.NT], 2020.
%F a(n) = A334543(n) + A334544(n).
%e The first two primes of the form 6k-1 are 5 and 11, so we have a(1)=11. The next primes of this form are 17, 23, 29; the gaps 17-11 = 23-17 = 29-23 have size 6 which already occurred before; so nothing is added to the sequence. The next prime of this form is 41 and the gap size 41-29=12 has not occurred before, so a(2)=41.
%o (PARI) isFirstOcc=vector(9999,j,1); s=5; forprime(p=11,1e8,if(p%6!=5,next); g=p-s; if(isFirstOcc[g/6], print1(p", "); isFirstOcc[g/6]=0); s=p)
%Y Cf. A007528, A014320, A058320, A268930, A330855, A334543, A334544.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, May 05 2020
|
