A334545 Primes of the form 6k - 1 at the end of first-occurrence gaps in A334543.

11, 41, 131, 227, 383, 557, 1151, 1787, 4337, 6449, 7433, 8363, 9137, 12893, 35729, 37781, 58889, 59879, 97787, 105863, 130769, 148667, 153887, 180959, 220151, 328271, 402761, 407153, 416849, 542441, 780587, 1138367, 1294571, 1444463, 1463837, 1604951

Offset

1,1

Comments

Subsequence of A007528. Contains A268930 as a subsequence. First differs from A268930 at a(5)=383.

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) = A334543(n) + A334544(n).

Example

The first two primes of the form 6k-1 are 5 and 11, so we have a(1)=11. 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)=41.

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

Crossrefs

Cf. A007528, A014320, A058320, A268930, A330855, A334543, A334544.

Sequence in context: A027086 A075985 A356125 * A268930 A139933 A243892

Adjacent sequences: A334542 A334543 A334544 * A334546 A334547 A334548

Keyword

nonn

Author

Alexei Kourbatov, May 05 2020

Status

approved