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A321320 Largest power of 2 obtainable by partitioning the binary representation of n into consecutive blocks and then summing. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A175462 A133946 A286250

Adjacent sequences:  A321317 A321318 A321319 * A321321 A321322 A321323

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Nov 04 2018

STATUS

approved

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)