

A327190


For any n > 0: consider the different ways to split the binary representation of 2*n+1 into two nonempty parts, say with value x and y; a(n) is the least possible value of x * y.


2



1, 1, 3, 1, 3, 3, 7, 1, 3, 5, 7, 3, 9, 7, 15, 1, 3, 5, 7, 5, 11, 11, 15, 3, 9, 13, 21, 7, 21, 15, 31, 1, 3, 5, 7, 9, 11, 13, 15, 5, 15, 21, 23, 11, 27, 23, 31, 3, 9, 15, 21, 13, 33, 27, 45, 7, 21, 29, 49, 15, 45, 31, 63, 1, 3, 5, 7, 9, 11, 13, 15, 9, 19, 21
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OFFSET

1,3


COMMENTS

All terms are odd.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..8192


FORMULA

a(n) = 1 iff n is a power of 2.
a(n) = n iff n is a positive Mersenne number (A000225).  Bernard Schott, Aug 26 2019


EXAMPLE

For n=42:
 the binary representation of 85 is "1010101",
 there are 6 ways to split it:
 "1" and "010101": x=1 and y=21: 1 * 21 = 21,
 "10" and "10101": x=2 and y=21: 2 * 21 = 42,
 "101" and "0101": x=5 and y=5: 5 * 5 = 25,
 "1010" and "101": x=10 and y=5: 10 * 5 = 50,
 "10101" and "01": x=21 and y=1: 21 * 1 = 21,
 "101010" and "1": x=42 and y=1: 42 * 1 = 42,
 hence a(42) = 21.


PROG

(PARI) a(n) = my (v=oo, b=binary(2*n+1)); for (w=1, #b1, v=min(v, (fromdigits(b[1..w], 2) * fromdigits(b[w+1..#b], 2)))); v


CROSSREFS

See A327186 for other variants.
Cf. A000225.
Sequence in context: A151837 A331856 A163381 * A160123 A238784 A336765
Adjacent sequences: A327187 A327188 A327189 * A327191 A327192 A327193


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Aug 25 2019


STATUS

approved



