A275341 Positions of ones in A275737.

1, 2, 3, 5, 6, 8, 11, 13, 15, 18, 20, 23, 25, 28, 30, 33, 37, 39, 42, 46, 49, 52, 55, 58, 61, 64, 68, 71, 74, 78, 82, 85, 89, 92, 95, 99, 103, 107, 110, 114, 118, 121, 126, 129, 133, 137, 140, 144, 148, 153, 156, 160, 165, 168, 172, 176, 180, 184, 189, 193, 197

Offset

1,2

Comments

a(n) appears to be asymptotic to log((n+1)!). The question at MathOverflow discusses a related but more complicated sequence.

Links

Jinyuan Wang, Table of n, a(n) for n = 1..10000 (terms 1..1000 from G. C. Greubel)

Mats Granvik, What explains the asymptotic and the pattern in this sequence related to Riemann zeta zeros?.

Formula

a(n) is the positions of ones in round(im(zetazero(n + 1))/(2*Pi)) - round(im(zetazero(n))/(2*Pi)), where n starts at 1.

Example

The sequence A275737: round(im(zetazero(n + 1))/(2*Pi)) - round(im(zetazero(n))/(2*Pi)) where n=1,2,3,4,5, starts:
1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1,...
The positions of ones in that sequence are a(n):
1, 2, 3, 5, 6, 8, 11, 13, 15, 18, 20, 23, 25, 28, 30,...
Compare this to round(log((n+1)!)) A046654:
1, 2, 3, 5, 7, 9, 11, 13, 15, 18, 20, 23, 25, 28, 31,...

Mathematica

Flatten[Position[Differences[Round[Im[ZetaZero[Range[135]]]/(2*Pi)]], 1]]

Crossrefs

Cf. A046654, A275579, A275737.

Sequence in context: A294911 A179799 A247588 * A191884 A291693 A266542

Adjacent sequences: A275338 A275339 A275340 * A275342 A275343 A275344

Keyword

nonn

Author

Mats Granvik, Jul 28 2016

Status

approved