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

Author

Antti Karttunen, Aug 18 2014

Keywords

• nonn

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.

Crossrefs

One less than A159481.

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

Programs

Mathematica

Join[{0},Accumulate[Table[If[EvenQ[DigitCount[n,2,1]],1,0],{n,80}]]] (* Harvey P. Dale, Aug 01 2021 *)

Python

def A245710(n): return (n+1>>1)-((n+1).bit_count()&1&(n+1)^1) # Chai Wah Wu, Mar 01 2023

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.