

A331856


a(n) is the least value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.


3



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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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 kth 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: A246591 A173465 A151837 * A163381 A327190 A160123
Adjacent sequences: A331853 A331854 A331855 * A331857 A331858 A331859


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Jan 29 2020


STATUS

approved



