A279539 Sum of ceilings of natural logs of first n integers.

0, 1, 3, 5, 7, 9, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241, 246, 251, 256, 261, 266, 271, 276, 281, 286

Offset: 1

Author

Jeffrey Shallit, Dec 14 2016

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001855, which is the same sequence for base-2 logarithms.

Partial sums of A004233.

Programs

Mathematica

Accumulate[Ceiling[Log[Range[100]]]] (* Paolo Xausa, Jun 28 2024 *)

PARI

a(n) = sum(i=1, n, ceil(log(i))) \\ Felix Fröhlich, Dec 14 2016