|
%I #24 May 04 2020 21:25:57
%S 13,31,61,271,307,1381,1531,1987,2437,4423,7867,10243,16831,22273,
%T 24337,38557,40351,43543,69661,75511,100927,119047,171403,195691,
%U 204301,250423,480343,577807,590593,1164799,1207903,1278997,1382419,1468189,1526929,1890019,2314591
%N Primes 6k + 1 at the end of first-occurrence gaps in A330853.
%C Subsequence of A002476. Contains A268927 as a subsequence. First differs from A268927 at a(5)=307.
%C A330853 lists the corresponding gap sizes; see more comments there.
%H Alexei Kourbatov, <a href="/A330855/b330855.txt">Table of n, a(n) for n = 1..135</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) = A330853(n) + A330854(n).
%e The first two primes of the form 6k+1 are 7 and 13, so a(1)=13. The next prime 6k+1 is 19, and the gap 19-13=6 already occurred, so a new term is not added to the sequence. The next prime 6k+1 is 31, and the gap 31-19=12 is occurring for the first time; therefore a(2)=31.
%o (PARI) isFirstOcc=vector(9999,j,1); s=7; forprime(p=13,1e8, if(p%6!=1,next); g=p-s; if(isFirstOcc[g/6], print1(p", "); isFirstOcc[g/6]=0); s=p)
%Y Cf. A002476, A014320, A058320, A268927, A330853 (first-occurrence gap sizes), A330854 (primes beginning the first-occurrence gaps).
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Apr 27 2020
|
