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A086977
Increasing peaks in the prime gap sequence A000230.
4
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
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 *)
KEYWORD
nonn
AUTHOR
Harry J. Smith, Jul 26 2003
STATUS
approved