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A331856
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a(n) is the least value 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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0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 5, 7, 3, 7, 7, 15, 1, 3, 5, 7, 5, 11, 11, 15, 3, 7, 11, 15, 7, 15, 15, 31, 1, 3, 5, 7, 9, 11, 11, 15, 5, 11, 21, 23, 13, 23, 23, 31, 3, 7, 13, 15, 11, 23, 27, 31, 7, 15, 23, 31, 15, 31, 31, 63, 1, 3, 5, 7, 9, 11, 11, 15, 9, 19, 21
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listen;
history;
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internal format)
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n)^A023416(n) = A038573(n) (where a^k denotes the k-th iterate of a).
a(n) <= n with equality iff n belongs to A000225.
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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, the least being 3,
- 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 A331855 for the number of distinct values, and A331857 for the greatest value.
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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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