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A175096 Write n in binary (without leading 0's). a(n) = the number of distinct numerical values made by permutating the runs of 0's and the runs of 1's, such that the runs (of nonzero length) of 1's alternate with the runs (of nonzero length) of 0's. The permutated binary numbers (those not equal to n) may start with leading 0's. 1
1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 4, 2, 4, 1, 4, 2, 2, 2, 4, 1, 2, 2, 2, 1, 2, 1, 4, 2, 2, 2, 8, 2, 4, 2, 2, 3, 8, 3, 4, 2, 2, 2, 8, 1, 8, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2, 1, 4, 2, 4, 2, 8, 2, 4, 1, 6, 6, 4, 6, 8, 2, 4, 2, 6, 6, 6, 1, 6, 3, 8, 6, 6, 3, 8, 3, 4, 2, 2, 2, 8, 1, 4, 6, 4, 2, 8, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Each "run" of binary digit b (0 or 1) is bounded by digits equal to 1-b, or is bounded by the edge of the binary string (which is n written in binary).
For all odd n, the values of all permutations of binary n are themselves odd, since there are an odd number of runs (the first and last runs being of 1's).
LINKS
EXAMPLE
20 in binary is 10100. So we have a run of one 1, followed by a run of one 0, followed by a run of one 1, followed finally by a run of two 0's. The permutations of the runs of 0's and the run's of 1's form these distinct binary numbers: 00101 (5 in decimal), 01001 (9 in decimal), 10010 (18 in decimal), and 10100 (20 in decimal). So a(20) = 4 since there are 4 such permutations.
CROSSREFS
Sequence in context: A365460 A235644 A298475 * A111627 A008618 A339368
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Feb 01 2010
EXTENSIONS
Extended by Ray Chandler, Feb 07 2010
STATUS
approved

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)