A085500 Indices of primes where nondecreasing gaps occur.

1, 2, 3, 4, 6, 8, 9, 11, 15, 16, 18, 21, 23, 24, 30, 62, 66, 99, 154, 189, 217, 1059, 1183, 1532, 1663, 1831, 2225, 2810, 3385, 14357, 29040, 30802, 31545, 40933, 103520, 104071, 118505, 149689, 325852, 733588, 983015, 1094421, 1319945, 2850174, 6957876, 10539432, 10655462

Offset: 1

Author

Farideh Firoozbakht, Aug 15 2003

Keywords

• nonn

Comments

A005669 is a subsequence of this sequence.

References

• Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A8, pp. 31-39.

Links

• Jeff Young and Aaron Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224.

Crossrefs

Cf. A085237, A005669, A005250, A134266.

See also A214935(n) = A000720(A205827(n)), A241540(n) = A000720(A182514(n)).

Programs

Mathematica

f[n_] := Prime[n+1]-Prime[n]; v1={}; v2={}; Do[If[f[n]>=If[n==1, 1, Last[v2]], v=n; v1=Append[v1, n]; v2=Append[v2, f[v]]; Print[v1]], {n, 105000000}]

Formula

a(n) = A000720(A134266(n)). - M. F. Hasler, Apr 26 2014

Extensions

a(45)-a(47) from Amiram Eldar, Sep 05 2024