1,1

Contains A002386 as a subsequence. First differs from A002386 at a(7)=139. This sequence is a permutation of all positive terms of A000230, in increasing order. See A002386 and A005250 for more references and links.

Brian Kehrig, Table of n, a(n) for n = 1..777 (Terms 1..745 from Alexei Kourbatov).

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.

The Prime Gap List, First Occurrence Prime Gaps

a(n) = A335367(n) - A014320(n).

The first two primes are 2 and 3, and the first prime gap is 3 - 2 = 1; so a(1)=2. The next prime is 5, and the next gap is 5 - 3 = 2; this gap size has not occurred before, so a(2)=3. The next prime is 7, and the next gap is 7 - 5 = 2; the gap size 2 has already occurred before, so nothing is added to the sequence.

(PARI) my(isFirstOcc=vector(9999, j, 1), s=2); forprime(p=3, 1e8, my(g=p-s); if(isFirstOcc[g], print1(s, ", "); isFirstOcc[g]=0); s=p)

Cf. A000230, A002386, A014320, A330853, A330854, A334543, A334544, A335367.

Sequence in context: A129739 A359292 A163834 * A002386 A000230 A256454

Adjacent sequences: A335363 A335364 A335365 * A335367 A335368 A335369

Alexei Kourbatov, Jun 03 2020

approved