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

Author

Alexei Kourbatov, May 05 2020

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A007528, A014320, A058320, A268928, A330853, A334544, A334545.

Programs

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)

Formula

a(n) = A334545(n) - A334544(n).