OFFSET
0,3
COMMENTS
Numbers that are sums of distinct powers of 100. - David Wasserman, Feb 26 2008
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..8191
David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version
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.
FORMULA
a(n) = A062033(n)/10, i.e., with final zero removed.
G.f.: (1/(1 - x))*Sum_{k>=0} 100^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
EXAMPLE
a(11)=1000101, since 11 in binary is 1011 and binary carryless sum of 1011000, 0, 10110 and 1011 is 1000101.
MATHEMATICA
With[{k = 100}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 5]]] (* Michael De Vlieger, Oct 29 2022 *)
PROG
(PARI) a(n) = fromdigits(binary(n), 100); \\ Ruud H.G. van Tol, Dec 05 2022
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Jul 03 2001
EXTENSIONS
More terms from David Wasserman, Feb 26 2008
STATUS
approved