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A331852
a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise XOR operator to the numbers represented by the blocks.
2
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 9, 9, 10, 10, 9, 9, 10, 10, 11, 11, 11, 11, 9, 9, 8, 8, 7, 7, 10, 10, 10, 10, 11, 11, 10, 10, 11, 11, 11, 11, 12
OFFSET
0,3
FORMULA
a(2^k) = k+1 for any k >= 0.
Apparently a(2^k-1) = A038348(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 XOR 2 = 3
"11" and "0" -> 3 XOR 0 = 3
"1" and "1" and "0" -> 1 XOR 1 XOR 0 = 0
- we have 3 distinct values,
- hence a(6) = 3.
PROG
(PARI) See Links section.
CROSSREFS
See A331851 for similar sequences.
Cf. A038348.
Sequence in context: A182008 A375024 A106457 * A103128 A156080 A334233
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 29 2020
STATUS
approved