A321320 Largest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing.

1, 2, 2, 4, 2, 2, 4, 8, 2, 4, 4, 2, 4, 4, 8, 16, 2, 4, 4, 4, 4, 8, 8, 2, 4, 8, 8, 4, 8, 8, 16, 32, 2, 4, 4, 8, 4, 8, 8, 4, 4, 4, 8, 8, 8, 16, 16, 2, 4, 8, 8, 8, 8, 8, 16, 4, 8, 16, 16, 8, 16, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 8, 16, 16, 4, 4, 8

Offset

1,2

Links

Table of n, a(n) for n=1..82.

E. Berlekamp, J. Buhler, Puzzle 6, Puzzles column, Emissary Fall (2011) 9.

Steve Butler, Ron Graham, and Richard Strong, Inserting plus signs and adding, Amer. Math. Monthly 123 (3) (2016), 274-279.

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).

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 the largest power of 2 is 4.

Crossrefs

Cf. A321318, A321319, A321321.

Sequence in context: A213431 A331985 A261891 * A366808 A175462 A133946

Adjacent sequences: A321317 A321318 A321319 * A321321 A321322 A321323

Keyword

nonn

Author

Jeffrey Shallit, Nov 04 2018

Status

approved