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A335367 Primes at the end of the first-occurrence gaps in A014320. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)