A334544 Primes of the form 6k - 1 preceding the first-occurrence gaps in A334543.

5, 29, 113, 197, 359, 521, 1109, 1733, 4289, 6389, 7349, 8297, 9059, 12821, 35603, 37691, 58787, 59771, 97673, 105767, 130649, 148517, 153749, 180797, 220019, 328127, 402593, 406907, 416693, 542261, 780401, 1138127, 1294367, 1444271, 1463621, 1604753

Offset: 1

Author

Alexei Kourbatov, May 05 2020

Keywords

• nonn

Comments

Subsequence of A007528. Contains A268929 as a subsequence. First differs from A268929 at a(5)=359.

A334543 lists the corresponding gap sizes; see more comments there.

Examples

			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.
		

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, A268929, A330854, A334543, 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(s", "); isFirstOcc[g/6]=0); s=p)

Formula

a(n) = A334545(n) - A334543(n).