A335367 Primes at the end of the first-occurrence gaps in A014320.

3, 5, 11, 29, 97, 127, 149, 211, 541, 907, 1151, 1361, 1693, 1847, 2503, 2999, 4327, 5623, 9587, 15727, 16183, 19373, 19661, 28277, 30631, 31469, 31957, 34123, 35671, 43391, 44351, 81509, 82129, 89753, 134581, 156007, 162209, 173429, 188107, 212777, 265703

Offset

1,1

Comments

Contains A000101 as a subsequence. First differs from A000101 at a(7)=149. See A000101, A002386 and A005250 for more references and links.

Links

Alexei Kourbatov, Table of n, a(n) for n = 1..745 (primes < 2^64)

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) = A335366(n) + A014320(n).

Example

The first two primes are 2 and 3, and the first prime gap is 3 - 2 = 1; so a(1)=3. The next prime is 5, and the next gap is 5 - 3 = 2; this gap size has not occurred before, so a(2)=5. 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.

Prog

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

Crossrefs

Cf. A000101, A002386, A005250, A014320, A330853, A330854, A334543, A334544, A335366.

Sequence in context: A168607 A057735 A095302 * A000101 A253899 A037152

Adjacent sequences: A335364 A335365 A335366 * A335368 A335369 A335370

Keyword

nonn

Author

Alexei Kourbatov, Jun 03 2020

Status

approved