OFFSET

1,1

COMMENTS

LINKS

Alexei Kourbatov, Table of n, a(n) for n = 1..135

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.

EXAMPLE

The first two primes of the form 6k + 1 are 7 and 13, so a(1) = 7. The next prime of that form is 19, and the gap 19 - 13 = 6 already occurred; so a new term is not added to the sequence. The next prime of the form 6k + 1 is 31, and the gap 31 - 19 = 12 is occurring for the first time; therefore a(2) = 19.

The gap between 241 and the next prime of the form 6k + 1 (271) is 30. So 241 is in the sequence.

Although the gap between 283 and 307 is only 24 (which is less than 30), the gap is of a size not previously encountered. So 283 is in the sequence.

PROG

(PARI) isFirstOcc=vector(9999, j, 1); s=7; forprime(p=13, 1e8, if(p%6!=1, next); g=p-s; if(isFirstOcc[g/6], print1(s", "); isFirstOcc[g/6]=0); s=p)

CROSSREFS

KEYWORD

nonn

AUTHOR

Alexei Kourbatov, Apr 27 2020

STATUS

approved