A079947 Partial sums of A030300.

1, 1, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36

Offset

1,4

Links

Kevin Ryde, Table of n, a(n) for n = 1..8192

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, pp. 49-50.

Formula

a(n) = (n+1+(2/3)*(4^e_4-1)+(-1)^e_2*(n-1-2*(4^e_4-1)))/2 where e_4=floor(log[4](n)) and e_2=floor(log[2](n))=floor(log[4](n^2)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 22 2003

a(n) = n - A079954(n). Let k=A000523(n), then a(n) = n-A000975(k) if k even, or a(n) = A000975(k) if k odd. - Kevin Ryde, Jul 13 2019

Mathematica

Accumulate@ Flatten@ Table[1 - Mod[n, 2], {n, 0, 6}, {2^n}] (* Michael De Vlieger, Oct 29 2022 *)

Prog

(PARI) a(n) = my(k=logint(n, 2), p=(2<<k)\3); if(bittest(k, 0), p, n-p); /* Kevin Ryde, Jul 13 2019 */
(Python)
def A079947(n): return n-((1<<k)-2)//3 if (k:=n.bit_length())&1 else ((1<<k)-1)//3 # Chai Wah Wu, Jan 30 2023

Crossrefs

Sequence in context: A168092 A210032 A093392 * A094699 A194259 A246264

Adjacent sequences: A079944 A079945 A079946 * A079948 A079949 A079950

Keyword

nonn

Author

N. J. A. Sloane, Feb 22 2003

Status

approved