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A306922 Number of distinct powers of two obtained by breaking the binary representation of n into consecutive blocks, and then adding the numbers represented by the blocks. 1
1, 2, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 2, 5, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 6, 1, 2, 1, 3, 1, 2, 2, 2, 1, 1, 2, 2, 2, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 7, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

1's appear at indices given by A321321.

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000

Elwyn Berlekamp and Joe P. Buhler, Puzzle 6, Puzzles column, Emissary, MSRI Newsletter, Fall 2011, Page 9, Problem 6.

Reddit user HarryPotter5777, Partition a binary string so sum of chunks is a power of two. (Proposed proof that a(n) > 0 for all n.)

EXAMPLE

For n = 46, the a(46) = 3 powers of two that come from the partition of "101110" are 4, 8, and 16:

[10, 1110]         -> [2, 14]            -> 16

[1, 0, 1, 110]     -> [1, 0, 1, 6]       -> 8

[101, 1, 10]       -> [5, 1, 2]          -> 8

[1, 0, 111, 0]     -> [1, 0, 7, 0]       -> 8

[101, 11, 0]       -> [5, 3, 0]          -> 8

[1, 0, 1, 1, 1, 0] -> [1, 0, 1, 1, 1, 0] -> 4

CROSSREFS

Cf. A306921, A321318, A321319, A321320, A321321.

Sequence in context: A326674 A331184 A333768 * A331181 A328917 A265917

Adjacent sequences:  A306919 A306920 A306921 * A306923 A306924 A306925

KEYWORD

nonn,base

AUTHOR

Peter Kagey, Mar 16 2019

STATUS

approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)