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A245710
Number of nonzero evil numbers <= n, see A001969.
8
0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 12, 13, 13, 14, 15, 15, 15, 16, 17, 17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 22, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 27, 28, 29, 29, 30, 30, 30, 31, 31, 32, 33, 33, 34, 34, 34, 35, 36
OFFSET
0,6
LINKS
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 52.
FORMULA
a(0) = 0, and for n >= 1, a(n) = A010059(n) + a(n-1). [Partial sums of A010059, after ignoring the first one at zero].
a(n) = n - A115384(n).
a(n) = A159481(n)-1.
MATHEMATICA
Join[{0}, Accumulate[Table[If[EvenQ[DigitCount[n, 2, 1]], 1, 0], {n, 80}]]] (* Harvey P. Dale, Aug 01 2021 *)
PROG
(Scheme, two alternative implementations)
;; With memoizing definec-macro:
(definec (A245710 n) (if (zero? n) n (+ (A010059 n) (A245710 (- n 1)))))
(define (A245710 n) (- n (A115384 n)))
(Python)
def A245710(n): return (n+1>>1)-((n+1).bit_count()&1&(n+1)^1) # Chai Wah Wu, Mar 01 2023
CROSSREFS
One less than A159481.
Sequence in context: A137580 A340068 A196369 * A137512 A157943 A267098
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 18 2014
STATUS
approved