A103813 Partial sums of A102370.

0, 3, 9, 14, 18, 33, 43, 52, 60, 71, 85, 98, 126, 149, 167, 184, 200, 219, 241, 262, 282, 313, 339, 364, 388, 415, 445, 506, 550, 589, 623, 656, 688, 723, 761, 798, 834, 881, 923, 964, 1004, 1047, 1093, 1138, 1198, 1253, 1303, 1352, 1400, 1451, 1505, 1558, 1610, 1673

Offset: 0

Author

N. J. A. Sloane and David Applegate, Apr 01 2005

Keywords

• nonn
• base

References

• Hardy and Wright, Sect. 18.2, for definition of average order.

Links

• David Applegate, Benoit Cloitre, Philippe Deléham, and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
• David Applegate, Benoit Cloitre, Philippe Deléham, and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Crossrefs

Cf. A102370.

Programs

Mathematica

Accumulate[f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^k]; k++ ]; s]; Table[ f[n] + n, {n, 0, 53}] ] (* James C. McMahon, Jan 21 2024 *)

Formula

The average order of A102370(n) is n + O(log n).