A334543 First occurrences of gaps between primes 6k - 1: gap sizes.

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

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