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A268678
Distinct values in A268395; partial sums of A268679.
7
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
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. A268677 (complement).
Cf. A268680 (least monotonic left inverse).
Cf. A268712.
Cf. also A004128.
Sequence in context: A066542 A003310 A038525 * A057201 A242965 A266796
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 10 2016
STATUS
approved