A268395 Partial sums of A268389.

0, 0, 0, 1, 1, 3, 4, 4, 4, 5, 7, 7, 8, 8, 8, 11, 11, 15, 16, 16, 18, 18, 18, 19, 20, 20, 20, 22, 22, 23, 26, 26, 26, 27, 31, 31, 32, 32, 32, 34, 36, 36, 36, 37, 37, 40, 41, 41, 42, 42, 42, 47, 47, 48, 50, 50, 50, 52, 53, 53, 56, 56, 56, 57, 57, 59, 60, 60, 64, 64, 64, 65, 66, 66, 66, 69, 69, 70, 72, 72, 74, 74, 74, 75, 75, 81

Offset: 0

Author

Antti Karttunen, Feb 10 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A048631, A268389, A268672.

Cf. A268678 (with duplicates removed), A268677 (numbers that do not occur here).

Cf. A268708, A268709, A268710.

Cf. also A054861.

Programs

Mathematica

f[n_] := Which[n == 1, 0, OddQ@ #, 0, EvenQ@ #, 1 + f[#/2]] &@ Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; Accumulate@ Array[f, {85}] (* Michael De Vlieger, Feb 12 2016, after Jan Mangaldan at A006068 *)

Formula

a(0) = 0, for n >= 1, a(n) = A268389(n) + a(n-1).

Other identities. For all n >= 0:

a(n) = A268389(A048631(n)).

a(n) = n - A268672(n).