The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A330853 First occurrences of gaps between primes 6k+1: gap sizes. 10
 6, 12, 18, 30, 24, 54, 42, 36, 48, 60, 78, 66, 72, 84, 90, 96, 114, 102, 162, 108, 126, 120, 132, 150, 138, 144, 174, 168, 156, 192, 204, 180, 198, 252, 270, 216, 222, 186, 228, 210, 240, 282, 246, 234, 276, 264, 258, 312, 330, 318, 288, 306, 294, 336, 300, 378 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Contains A268925 as a subsequence. Conjecture: the sequence is a permutation of all positive multiples of 6, i.e., all positive terms of A008588. Conjecture: a(n) = O(n). See arXiv:2002.02115 (sect.7) for discussion. 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. FORMULA a(n) = A330855(n) - A330854(n). EXAMPLE The first primes of the form 6k+1 are 7 and 13, so a(1)=13-7=6. The next prime 6k+1 is 19, and the gap 19-13=6 already occurred, so a new term is not added to the sequence. The next prime 6k+1 is 31, and the gap 31-19=12 is occurring for the first time; therefore a(2)=12. 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(g", "); isFirstOcc[g/6]=0); s=p) CROSSREFS Cf. A002476, A014320, A058320, A330854 (primes 6k+1 preceding the first-occurrence gaps), A330855 (primes 6k+1 at the end of the first-occurrence gaps). Sequence in context: A088345 A057826 A334543 * A268657 A232742 A268928 Adjacent sequences:  A330850 A330851 A330852 * A330854 A330855 A330856 KEYWORD nonn AUTHOR Alexei Kourbatov, Apr 27 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 5 17:54 EDT 2021. Contains 343572 sequences. (Running on oeis4.)