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A327189
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 x + y.
3
0, 1, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 5
OFFSET
0,4
LINKS
FORMULA
a(n) = 1 iff n is a power of 2.
a(n) = 2 iff n = 2^k + 1 for some k > 0.
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: 0 + 42 = 42,
- "1" and "01010": x=1 and y=10: 1 + 10 = 11,
- "10" and "1010": x=2 and y=10: 2 + 10 = 12,
- "101" and "010": x=5 and y=2: 5 + 2 = 7,
- "1010" and "10": x=10 and y=2: 10 + 2 = 12,
- "10101" and "0": x=21 and y=0: 21 + 0 = 21,
- "101010" and "": x=42 and y=0: 42 + 0 = 42,
- hence a(42) = 7.
PROG
(PARI) a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=min(v, (fromdigits(b[1..w], 2) + fromdigits(b[w+1..#b], 2)))); v
CROSSREFS
See A327186 for other variants.
Sequence in context: A194865 A075425 A330960 * A255045 A194103 A074294
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Aug 25 2019
STATUS
approved