A331851 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then multiplying the numbers represented by the blocks.
1, 1, 2, 2, 2, 4, 3, 3, 2, 5, 4, 7, 3, 7, 4, 5, 2, 6, 5, 9, 4, 7, 7, 11, 3, 9, 7, 11, 4, 11, 6, 7, 2, 7, 6, 11, 5, 11, 9, 14, 4, 11, 7, 15, 7, 15, 11, 17, 3, 11, 9, 13, 7, 15, 11, 19, 4, 14, 11, 19, 6, 17, 8, 11, 2, 8, 7, 13, 6, 13, 11, 17, 5, 10, 11, 21, 9
Offset: 0
Examples
For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
"110" -> 6
"1" and "10" -> 1*2 = 2
"11" and "0" -> 3*0 = 0
"1" and "1" and "0" -> 1*1*0 = 0
- we have 3 distinct values,
- hence a(6) = 3.
Links
Crossrefs
Programs
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PARI
See Links section.
Formula
a(2^k) = 2 for any k > 0.
a(2^k+1) = k+2 for any k > 1.
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