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

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

Ferenc Adorjan, Table of n, a(n) for n=1..999 based on Thomas R. Nicely's web page

C. K. Caldwell, The prime pages

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]

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

Adjacent sequences: A014318 A014319 A014320 * A014322 A014323 A014324

Keyword

nonn

Author

Hynek Mlcousek (hynek(AT)dior.ics.muni.cz)

Extensions

More terms from Ferenc Adorjan (ferencadorjan(AT)gmail.com) May 17 2007

Status

approved