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%I #15 Jun 02 2020 22:13:07
%S 5,29,113,197,359,521,1109,1733,4289,6389,7349,8297,9059,12821,35603,
%T 37691,58787,59771,97673,105767,130649,148517,153749,180797,220019,
%U 328127,402593,406907,416693,542261,780401,1138127,1294367,1444271,1463621,1604753
%N Primes of the form 6k - 1 preceding the first-occurrence gaps in A334543.
%C Subsequence of A007528. Contains A268929 as a subsequence. First differs from A268929 at a(5)=359.
%C A334543 lists the corresponding gap sizes; see more comments there.
%H Alexei Kourbatov, <a href="/A334544/b334544.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) = A334545(n) - A334543(n).
%e The first two primes of the form 6k-1 are 5 and 11; we have a(1)=5. 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)=29.
%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(s", "); isFirstOcc[g/6]=0); s=p)
%Y Cf. A007528, A014320, A058320, A268929, A330854, A334543, A334545.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, May 05 2020
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