A245710 Number of nonzero evil numbers <= n, see A001969.

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

Michael De Vlieger, Table of n, a(n) for n = 0..10000

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.

Cf. A001969, A010059, A115384, A246159, A246162.

Sequence in context: A137580 A340068 A196369 * A137512 A157943 A267098

Adjacent sequences: A245707 A245708 A245709 * A245711 A245712 A245713

Keyword

nonn

Author

Antti Karttunen, Aug 18 2014

Status

approved