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A331854 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise OR operator to the numbers represented by the blocks. 2
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 5, 5, 4, 4, 5, 5, 7, 6, 7, 6, 7, 6, 7, 7, 8, 7, 7, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 8, 9, 8, 9, 7, 10, 9, 9, 8, 9, 9, 11, 10, 10, 9, 11, 10, 11, 11, 11, 10, 9, 9, 6, 6, 7, 7, 11, 10, 12, 10, 12, 11, 12, 10, 14, 10, 13, 11, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(2^k) = k+1 for any k >= 0.
a(2^k-1) = k for any k > 0.
EXAMPLE
For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
"110" -> 6
"1" and "10" -> 1 OR 2 = 3
"11" and "0" -> 3 OR 0 = 3
"1" and "1" and "0" -> 1 OR 1 OR 0 = 1
- we have 3 distinct values,
- hence a(6) = 3.
PROG
(PARI) See Links section.
CROSSREFS
See A331851 for similar sequences.
Sequence in context: A156251 A116458 A354166 * A093875 A329242 A266193
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 29 2020
STATUS
approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)