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

Author

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

Keywords

• nonn

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

Crossrefs

Cf. A014320.

Equals A058320(n+1)/2.

Inverse: A130264, Cf. A086979.

Programs

Mathematica

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

Extensions

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