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

0,3

Links

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

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.

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 *)

Prog

(Scheme, two variants, the first one using also memoizing-macro definec)
(definec (A268678 n) (if (zero? n) n (+ (A268679 n) (A268678 (- n 1)))))
(define (A268678 n) (A268395 (A001969 (+ 1 n))))

Crossrefs

Cf. A001969, A268395, A268679.

Cf. A268677 (complement).

Cf. A268680 (least monotonic left inverse).

Cf. A268712.

Cf. also A004128.

Sequence in context: A066542 A003310 A038525 * A057201 A242965 A266796

Adjacent sequences: A268675 A268676 A268677 * A268679 A268680 A268681

Keyword

nonn

Author

Antti Karttunen, Feb 10 2016

Status

approved