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A331853
a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise AND operator to the numbers represented by the blocks.
2
1, 1, 2, 2, 2, 3, 2, 2, 2, 3, 3, 4, 2, 3, 3, 3, 2, 3, 3, 4, 2, 3, 3, 4, 2, 3, 3, 5, 2, 3, 3, 3, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 6, 2, 3, 3, 5, 3, 4, 4, 5, 2, 3, 3, 5, 3, 4, 4, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 6, 2, 3, 3, 4, 3, 4, 4
OFFSET
0,3
FORMULA
a(2^k) = 2 for any k > 0.
a(2^k-1) = A008619(k+1) 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 AND 2 = 0
"11" and "0" -> 3 AND 0 = 0
"1" and "1" and "0" -> 1 AND 1 AND 0 = 0
- we have 2 distinct values,
- hence a(6) = 2.
PROG
(PARI) See Links section.
CROSSREFS
See A331851 for similar sequences.
Cf. A008619.
Sequence in context: A109709 A125604 A216685 * A187184 A301375 A325273
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 29 2020
STATUS
approved