A086979 -id:A086979 - cp's OEIS frontend

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

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

nonn

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

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

Cf. A014320.
Equals A058320(n+1)/2.
Inverse: A130264, Cf. A086979.

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

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

A086977 Increasing peaks in the prime gap sequence A000230.

Original entry on oeis.org

199, 1831, 5591, 30593, 81463, 82073, 162143, 173359, 404597, 542603, 544279, 1100977, 1444309, 2238823, 5845193, 6752623, 6958667, 11981443, 13626257, 49269581, 83751121, 147684137, 166726367, 378043979, 895858039, 1872851947

Offset: 1

Harry J. Smith, Jul 26 2003

nonn

a(n) is the smaller of the two consecutive primes having a late occurring prime gap g = p_k+1 - p_k. All even gaps smaller than g occur at a smaller prime. Also, the next even gap g+2 also occurs earlier.

			1831 is in this list because the next prime is 1847, giving a prime gap of 16. All even gaps less than 16 occur before this (for smaller primes) and the next even gap, 18, also occurs earlier.

P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
Eric Weisstein's World of Mathematics, Prime Gaps

Cf. A000230, A001223, A001632, A038664, A086978, A086979, A086980, A002386.

lst={};b=max=2;Do[a=2;While[NextPrime@a-a!=2n,a=NextPrime@a];If[a=max,AppendTo[lst,b]];b=a;If[b>max,max=b],{n,40}];lst (* Giorgos Kalogeropoulos, Aug 18 2021 *)

A086980 Late occurring prime gaps in the prime gap sequence A001223.

Original entry on oeis.org

12, 16, 32, 38, 46, 56, 66, 70, 74, 80, 88, 94, 102, 108, 116, 124, 134, 144, 150, 158, 166, 186, 194, 200, 228, 256, 264, 278, 294, 298, 316, 328, 334, 362, 370, 388, 422, 436, 442, 452, 466, 472, 482, 488, 510, 520, 536, 568, 576, 580, 590, 608, 628, 632

Offset: 1

Harry J. Smith, Jul 26 2003

nonn

a(n) is the gap g = p_k+1 - p_k between consecutive primes with all even gaps smaller than g occurring at a smaller prime and the next even gap g+2 also occurring earlier.

			16 is in this list because the first time a prime gap of 16 occurs is between consecutive primes 1831 and 1847. All even prime gaps less than 16 occur for a smaller prime. The next even prime gap of 18 also occurs earlier.

P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
Eric Weisstein's World of Mathematics, Prime Gaps

Cf. A000230, A001223, A001632, A038664, A086977, A086978, A086979, A002386.

A086978 Increasing peaks in the prime gap sequence A001632.

Original entry on oeis.org

211, 1847, 5623, 30631, 81509, 82129, 162209, 173429, 404671, 542683, 544367, 1101071, 1444411, 2238931, 5845309, 6752747, 6958801, 11981587, 13626407, 49269739, 83751287, 147684323, 166726561, 378044179, 895858267, 1872852203

Offset: 1

Harry J. Smith, Jul 26 2003

nonn

a(n) is the larger of the two consecutive primes having a late occurring prime gap g = p_k+1 - p_k. All even gaps smaller than g occur at a smaller prime. Also, the next even gap g+2 also occurs earlier.

			1847 is in this list because the previous prime is 1831, giving a prime gap of 16. All even gaps less than 16 occur before this (for smaller primes) and the next even gap, 18, also occurs earlier.

P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
Eric Weisstein's World of Mathematics, Prime Gaps.

Cf. A000230, A001223, A001632, A038664, A086977, A086979, A086980, A002386.

cp's OEIS Frontend

A014321 The next new gap between successive odd primes (divided by 2).

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A086977 Increasing peaks in the prime gap sequence A000230.

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A086980 Late occurring prime gaps in the prime gap sequence A001223.

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A086978 Increasing peaks in the prime gap sequence A001632.

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