A268383 Least monotonic left inverse of A268412.

0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 17, 18, 19, 19, 20, 21, 22, 22, 22, 22, 23, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 35, 35, 35, 36, 37, 38, 39, 39, 40, 41, 42, 42, 42, 42, 43, 43, 44, 45, 46

Offset: 0

Author

Antti Karttunen, Feb 05 2016

Keywords

• nonn

Comments

a(n) = Number of nonzero "balanced evil numbers" (A268412 without its initial zero) in range [0..n].

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Crossrefs

Cf. A268411, A268412, A268382.

Programs

Python

A268383_list = [0]
for i in range(1,10**6):
    A268383_list.append(A268383_list[-1]+1-len(list(filter(bool,format(i,'b').split('0')))) % 2) # Chai Wah Wu, Mar 01 2016

Formula

a(0) = 0; for n >= 1, a(n) = (1-A268411(n)) + a(n-1).

Other identities. For all n >= 0:

a(A268412(n)) = n.

a(n) = n - A268382(n).