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A334544 Primes of the form 6k - 1 preceding the first-occurrence gaps in A334543. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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) - A334543(n).

EXAMPLE

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.

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

CROSSREFS

Cf. A007528, A014320, A058320, A268929, A330854, A334543, A334545.

Sequence in context: A057721 A085151 A119494 * A268929 A268244 A297632

Adjacent sequences:  A334541 A334542 A334543 * A334545 A334546 A334547

KEYWORD

nonn

AUTHOR

Alexei Kourbatov, May 05 2020

STATUS

approved

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Last modified May 5 19:05 EDT 2021. Contains 343573 sequences. (Running on oeis4.)