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A331855
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a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.
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4
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1, 1, 2, 1, 3, 3, 3, 1, 4, 6, 5, 4, 5, 4, 4, 1, 5, 10, 9, 9, 8, 8, 9, 5, 7, 9, 8, 5, 7, 5, 5, 1, 6, 15, 14, 16, 12, 16, 18, 12, 11, 16, 13, 12, 15, 13, 14, 6, 9, 16, 15, 13, 13, 12, 12, 6, 10, 12, 11, 6, 9, 6, 6, 1, 7, 21, 20, 25, 18, 27, 30, 22, 16, 27, 25
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listen;
history;
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internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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a(2^k-1) = 1 for any k >= 0.
a(2^k) = k+1 for any k >= 0.
a(2^k+1) = A000217(k) for any k > 0.
a(2^k+2) = A000096(k-1) for any k > 3.
a(2^k+3) = (k-1)^2 for any k > 1.
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EXAMPLE
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For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
"110" -> "011" -> 3
"1" and "10" -> "1" and "01" -> 5
"11" and "0" -> "11" and "0" -> 6
"1" and "1" and "0" -> "1" and "1" and "0" -> 6
- we have 3 distinct values,
- hence a(6) = 3.
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A331856 and A331857 for the least and greatest values, respectively.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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