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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.)