A335366 Primes preceding the first-occurrence gaps in A014320.

2, 3, 7, 23, 89, 113, 139, 199, 523, 887, 1129, 1327, 1669, 1831, 2477, 2971, 4297, 5591, 9551, 15683, 16141, 19333, 19609, 28229, 30593, 31397, 31907, 34061, 35617, 43331, 44293, 81463, 82073, 89689, 134513, 155921, 162143, 173359, 188029, 212701, 265621

Offset: 1

Author

Alexei Kourbatov, Jun 03 2020

Keywords

• nonn

Comments

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.

Examples

			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.
		

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

Crossrefs

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

Programs

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)

Formula

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