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 A334543 First occurrences of gaps between primes 6k - 1: gap sizes. 9
 6, 12, 18, 30, 24, 36, 42, 54, 48, 60, 84, 66, 78, 72, 126, 90, 102, 108, 114, 96, 120, 150, 138, 162, 132, 144, 168, 246, 156, 180, 186, 240, 204, 192, 216, 198, 210, 174, 258, 252, 222, 234, 228, 318, 282, 264, 276, 342, 306, 294, 312, 270, 354, 372 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Contains A268928 as a subsequence. First differs from A268928 at a(5)=24. Conjecture: the sequence is a permutation of all positive multiples of 6, i.e., all positive terms of A008588. Conjecture: a(n) = O(n). See arXiv:2002.02115 (sect.7) for discussion. LINKS Alexei Kourbatov, Table of n, a(n) for n = 1..160 Alexei Kourbatov and Marek Wolf, On the first occurrences of gaps between primes in a residue class, arXiv preprint arXiv:2002.02115 [math.NT], 2020. FORMULA a(n) = A334545(n) - A334544(n). EXAMPLE The first two primes of the form 6k-1 are 5 and 11, so a(1)=11-5=6. 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 41-29=12 has not occurred before, so a(2)=12. PROG (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(g", "); isFirstOcc[g/6]=0); s=p) CROSSREFS Cf. A007528, A014320, A058320, A268928, A330853, A334544, A334545. Sequence in context: A270383 A088345 A057826 * A330853 A268657 A232742 Adjacent sequences:  A334540 A334541 A334542 * A334544 A334545 A334546 KEYWORD nonn AUTHOR Alexei Kourbatov, May 05 2020 STATUS approved

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Last modified May 5 19:06 EDT 2021. Contains 343573 sequences. (Running on oeis4.)