OFFSET
1,2
COMMENTS
Conjecture: With the exception of a(1) = 1 and a(17) = 31, all terms have a binary weight of 2 or 3. - Peter Kagey, Jun 14 2019
LINKS
Peter Kagey, Table of n, a(n) for n = 1..200
E. Berlekamp, J. Buhler, Puzzle 6, Puzzles column, Emissary Fall (2011) 9.
Steve Butler, Ron Graham, and Richard Stong, Collapsing numbers in bases 2, 3, and beyond, in The Proceedings of the Gathering for Gardner 10 (2012).
Steve Butler, Ron Graham, and Richard Strong, Inserting plus signs and adding, Amer. Math. Monthly 123 (3) (2016), 274-279.
EXAMPLE
For n = 13, we can partition its binary representation as follows (showing partition and sum of terms): (1101):13, (1)(101):6, (11)(01):4, (110)(1):7, (1)(1)(01):3, (1)(10)(1):4, (11)(0)(1):4, (1)(1)(0)(1):3. Thus there is only one possible power of 2, namely 4.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Nov 04 2018
STATUS
approved