A086977 Increasing peaks in the prime gap sequence A000230.

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

1,1

Comments

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.

References

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

Links

Table of n, a(n) for n=1..26.

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

Eric Weisstein's World of Mathematics, Prime Gaps

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A159064 A117594 A052188 * A324628 A216346 A289819

Adjacent sequences: A086974 A086975 A086976 * A086978 A086979 A086980

Keyword

nonn

Author

Harry J. Smith, Jul 26 2003

Status

approved