A321318 Number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then summing the numbers represented by the blocks.
1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 8, 8, 7, 7, 9, 9, 8, 8, 7, 7, 6, 6, 9, 9, 9, 9, 10, 10, 9, 9, 9, 9, 12, 12, 13, 13, 9, 9, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 12, 12, 11, 11, 7, 7, 11, 11, 12, 12, 13, 13, 12, 12, 15, 15, 15
Offset: 1
Examples
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 are 5 distinct values.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..16384
- Elwyn Berlekamp and Joe P. Buhler, Puzzle 6, Puzzles column, Emissary, MSRI Newsletter, Fall 2011, Page 9, Problem 6.
- 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.
- Rémy Sigrist, PARI program for A321318
Programs
-
PARI
See Links section