OFFSET
0,3
COMMENTS
Numbers without any base-8 digits greater than 1.
Every nonnegative n is a unique sum of the form a(p)+2a(q)+4a(r). This gives a one-to-one map of the set N_0 of all nonnegative integers to (N_0)^3. Furthermore, if, for a fixed positive integer m, to consider all sums of distinct powers of 2^m, then one can obtain a one-to-one map of the set N_0 to (N_0)^m. - Vladimir Shevelev, Nov 15 2008
LINKS
David A. Corneth, Table of n, a(n) for n = 0..9999 (first 1024 terms from T. D. Noe)
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. 45.
Michael Penn, "almost" a generating function..., YouTube video, 2020.
FORMULA
a(n) = Sum_{i=0..m} d(i)*8^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097254(n)/7.
a(2n) = 8*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*8^k. - Philippe Deléham, Oct 19 2011
G.f.: (1/(1 - x))*Sum_{k>=0} 8^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
EXAMPLE
a(7)=72 because 72_10 = 110_8.
PROG
(PARI) A033045(n, b=8)=subst(Pol(binary(n)), 'x, b) \\ M. F. Hasler, Feb 01 2016
(PARI) a(n) = fromdigits(binary(n), 8) \\ David A. Corneth, Dec 17 2020
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
More terms from Patrick De Geest, Dec 23 2000
STATUS
approved