A014321 - OEIS

%I #34 Aug 11 2024 14:46:30

%S 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,

%T 31,27,30,29,23,28,32,34,43,33,35,39,38,41,48,56,50,37,45,42,57,40,44,

%U 49,46,53,47,59,66,52,51,55,63,60,74,54,61,69,64,77,65,58,73,68,62,67

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

%C 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

%H Brian Kehrig, <a href="/A014321/b014321.txt">Table of n, a(n) for n = 1..747</a> (terms 1..641 from Ferenc Adorjan, terms from a(642) onward corrected by Brian Kehrig).

%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/">The prime pages</a>

%H Thomas R. Nicely, <a href="https://web.archive.org/web/20240329172002/https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a>

%H The Prime Gap List, <a href="https://primegap-list-project.github.io/lists/prime-gaps-first-occurrences/">First occurrence prime gaps</a>

%t DeleteDuplicates[Differences[Prime[Range[2,500000]]]]/2 (* _Harvey P. Dale_, Sep 15 2023 *)

%Y Cf. A014320.

%Y Equals A058320(n+1)/2.

%Y Inverse: A130264, Cf. A086979.

%K nonn

%O 1,2

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

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