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A334545 Primes of the form 6k - 1 at the end of first-occurrence gaps in A334543. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A195117 A027086 A075985 * A268930 A139933 A243892

Adjacent sequences:  A334542 A334543 A334544 * A334546 A334547 A334548

KEYWORD

nonn

AUTHOR

Alexei Kourbatov, May 05 2020

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)