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%I #23 Jan 22 2024 10:25:03
%S 0,3,9,14,18,33,43,52,60,71,85,98,126,149,167,184,200,219,241,262,282,
%T 313,339,364,388,415,445,506,550,589,623,656,688,723,761,798,834,881,
%U 923,964,1004,1047,1093,1138,1198,1253,1303,1352,1400,1451,1505,1558,1610,1673
%N Partial sums of A102370.
%D Hardy and Wright, Sect. 18.2, for definition of average order.
%H David Applegate, Benoit Cloitre, Philippe Deléham, and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].
%H David Applegate, Benoit Cloitre, Philippe Deléham, and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
%F The average order of A102370(n) is n + O(log n).
%t 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 *)
%Y Cf. A102370.
%K nonn,base
%O 0,2
%A _N. J. A. Sloane_ and _David Applegate_, Apr 01 2005
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