A268678 Distinct values in A268395; partial sums of A268679.

0, 1, 3, 4, 5, 7, 8, 11, 15, 16, 18, 19, 20, 22, 23, 26, 27, 31, 32, 34, 36, 37, 40, 41, 42, 47, 48, 50, 52, 53, 56, 57, 59, 60, 64, 65, 66, 69, 70, 72, 74, 75, 81, 82, 83, 86, 87, 89, 90, 92, 93, 98, 101, 102, 104, 105, 106, 108, 109, 113, 116, 117, 119, 120, 121, 123, 124, 127, 131, 132, 134, 135, 136, 138, 139, 142

Offset: 0

Author

Antti Karttunen, Feb 10 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768

Crossrefs

Cf. A001969, A268395, A268679.

Cf. A268677 (complement).

Cf. A268680 (least monotonic left inverse).

Cf. A268712.

Cf. also A004128.

Programs

Mathematica

f[n_] := Which[n == 1, 0, OddQ@ #, 0, EvenQ@ #, 1 + f[#/2]] &@ Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; Union@ Accumulate@ Array[f, {150}] (* Michael De Vlieger, Feb 12 2016, after Jan Mangaldan at A006068 *)

Formula

a(0) = 0, for n >= 1, a(n) = A268679(n) + a(n-1).

a(n) = A268395(A001969(1+n)).

Other identities. For all n >= 0:

A268680(a(n)) = n.