A014321 - OEIS

A014321

The next new gap between successive odd primes (divided by 2).

1, 2, 3, 4, 7, 5, 6, 9, 10, 11, 17, 12, 8, 13, 14, 15, 16, 18, 22, 21, 20, 26, 24, 19, 36, 25, 31, 27, 30, 29, 23, 28, 32, 34, 43, 33, 35, 39, 38, 41, 48, 56, 50, 37, 45, 42, 57, 40, 44, 49, 46, 53, 47, 59, 66, 52, 51, 55, 63, 60, 74, 54, 61, 69, 64, 77, 65, 58, 73, 68, 62, 67

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

If Polignac's conjecture holds (which is highly likely), then this sequence is a permutation of the positive integers. Even a weaker form of the conjecture would be enough: "Every even number occurs at least once as difference of subsequent primes". - Ferenc Adorjan (ferencadorjan(AT)gmail.com), May 17 2007

LINKS

Brian Kehrig, Table of n, a(n) for n = 1..747 (terms 1..641 from Ferenc Adorjan, terms from a(642) onward corrected by Brian Kehrig).

C. K. Caldwell, The prime pages

Thomas R. Nicely, First occurrence prime gaps

The Prime Gap List, First occurrence prime gaps

MATHEMATICA

DeleteDuplicates[Differences[Prime[Range[2, 500000]]]]/2 (* Harvey P. Dale, Sep 15 2023 *)

CROSSREFS

Cf. A014320.

Equals A058320(n+1)/2.

Inverse: A130264, Cf. A086979.

Sequence in context: A268131 A361646 A359051 * A175343 A239965 A072767