

A327193


For any n >= 0: consider the different ways to split the binary representation of n into two (possibly empty) parts, say with value x and y; a(n) is the greatest possible value of min(x, y).


3



0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 3, 0, 1, 2, 3, 2, 2, 2, 3, 1, 1, 2, 3, 3, 3, 3, 3, 0, 1, 2, 3, 4, 4, 4, 4, 2, 2, 2, 3, 4, 5, 5, 5, 1, 1, 2, 3, 4, 5, 6, 6, 3, 3, 3, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 4, 4, 4, 4, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 6
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OFFSET

0,11


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192


FORMULA

a(n) = 0 iff n = 0 or n is a power of 2.


EXAMPLE

For n=42:
 the binary representation of 42 is "101010",
 there are 7 ways to split it:
 "" and "101010": x=0 and y=42: min(0, 42) = 0,
 "1" and "01010": x=1 and y=10: min(1, 10) = 1,
 "10" and "1010": x=2 and y=10: min(2, 10) = 2,
 "101" and "010": x=5 and y=2: min(5, 2) = 2,
 "1010" and "10": x=10 and y=2: min(10, 2) = 2,
 "10101" and "0": x=21 and y=0: min(21, 0) = 0,
 "101010" and "": x=42 and y=0: min(42, 0) = 0,
 hence a(42) = 2.


PROG

(PARI) a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=max(v, min(fromdigits(b[1..w], 2), fromdigits(b[w+1..#b], 2)))); v


CROSSREFS

See A327186 for other variants.
Sequence in context: A164516 A016533 A122915 * A279522 A182592 A030298
Adjacent sequences: A327190 A327191 A327192 * A327194 A327195 A327196


KEYWORD

nonn,look,base


AUTHOR

Rémy Sigrist, Aug 25 2019


STATUS

approved



