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A268383
Least monotonic left inverse of A268412.
3
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
0,10
COMMENTS
a(n) = Number of nonzero "balanced evil numbers" (A268412 without its initial zero) in range [0..n].
LINKS
Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 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).
PROG
(Scheme, with memoization-macro definec)
(definec (A268383 n) (if (zero? n) n (+ (- 1 (A268411 n)) (A268383 (- n 1)))))
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 05 2016
STATUS
approved