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A335366 Primes preceding the first-occurrence gaps in A014320. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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

EXAMPLE

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.

PROG

(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)

CROSSREFS

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

Sequence in context: A088173 A129739 A163834 * A002386 A000230 A256454

Adjacent sequences:  A335363 A335364 A335365 * A335367 A335368 A335369

KEYWORD

nonn

AUTHOR

Alexei Kourbatov, Jun 03 2020

STATUS

approved

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Last modified April 18 03:59 EDT 2021. Contains 343072 sequences. (Running on oeis4.)