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A331856
a(n) is the least value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.
4
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
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..16384
Rémy Sigrist, PARI program for A331856
Index entries for sequences related to binary expansion of n
FORMULA
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.
EXAMPLE
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.
PROG
(PARI) See Links section.
CROSSREFS
See A331855 for the number of distinct values, and A331857 for the greatest value.
Cf. A000225, A023416, A038573.
Sequence in context: A151837 A356354 A355339 * A163381 A373886 A327190
Adjacent sequences: A331853 A331854 A331855 * A331857 A331858 A331859
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 29 2020
STATUS
approved

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Last modified September 28 13:00 EDT 2024. Contains 376297 sequences.
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