

A327195


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^2  y^2).


3



0, 1, 1, 0, 1, 0, 3, 8, 1, 0, 0, 5, 9, 8, 5, 0, 1, 0, 0, 5, 12, 21, 21, 16, 9, 8, 5, 0, 7, 16, 27, 40, 1, 0, 0, 5, 0, 9, 20, 33, 25, 24, 21, 16, 9, 0, 11, 24, 9, 8, 5, 0, 7, 11, 0, 13, 49, 48, 45, 40, 33, 24, 13, 0, 1, 0, 0, 5, 0, 9, 20, 15, 48, 65, 77, 72, 65
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OFFSET

0,7


LINKS

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


FORMULA

a(n) = 0 iff n = 0 or n belongs to A175468.
a(n) = 1 iff 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: abs(0^2  42^2) = 1764,
 "1" and "01010": x=1 and y=10: abs(1^2  10^2) = 99,
 "10" and "1010": x=2 and y=10: abs(2^2  10^2) = 96,
 "101" and "010": x=5 and y=2: abs(5^2  2^2) = 21,
 "1010" and "10": x=10 and y=2: abs(10^2  2^2) = 96,
 "10101" and "0": x=21 and y=0: abs(21^2  0^2) = 441,
 "101010" and "": x=42 and y=0: abs(42^2  0^2) = 1764,
 hence a(42) = 21.


PROG

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


CROSSREFS

See A327186 for other variants.
Cf. A175468.
Sequence in context: A225802 A156827 A330963 * A140272 A210962 A021728
Adjacent sequences: A327192 A327193 A327194 * A327196 A327197 A327198


KEYWORD

nonn,look,base


AUTHOR

Rémy Sigrist, Aug 25 2019


STATUS

approved



