

A327191


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 least possible value of abs(x  y).


3



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

0,8


LINKS

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


FORMULA

a(n) = 0 iff n = 0 or n belongs to A175468.


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: abs(0  42) = 42,
 "1" and "01010": x=1 and y=10: abs(1  10) = 9,
 "10" and "1010": x=2 and y=10: abs(2  10) = 8,
 "101" and "010": x=5 and y=2: abs(5  2) = 3,
 "1010" and "10": x=10 and y=2: abs(10  2) = 8,
 "10101" and "0": x=21 and y=0: abs(21  0) = 21,
 "101010" and "": x=42 and y=0: abs(42  0) = 42,
 hence a(42) = 3.


PROG

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


CROSSREFS

See A327186 for other variants.
Cf. A175468.
Sequence in context: A301570 A301567 A115363 * A036867 A036866 A144225
Adjacent sequences: A327188 A327189 A327190 * A327192 A327193 A327194


KEYWORD

nonn,look,base


AUTHOR

Rémy Sigrist, Aug 25 2019


STATUS

approved



