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 A327186 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 OR y (where OR denotes the bitwise OR operator). 12
 0, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 3, 3, 3, 3, 3, 1, 1, 2, 3, 5, 5, 6, 7, 3, 3, 3, 3, 7, 7, 7, 7, 1, 1, 2, 3, 4, 5, 6, 7, 5, 5, 7, 7, 5, 5, 7, 7, 3, 3, 3, 3, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 1, 2, 3, 4, 5, 6, 7, 9, 9, 10, 11, 12, 13, 14, 15, 5, 5, 7, 7, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8192 FORMULA a(n) = 1 iff n = 2^k or 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 OR 42 = 42,    - "1" and "01010": x=1 and y=10: 1 OR 10 = 11,    - "10" and "1010": x=2 and y=10: 2 OR 10 = 10,    - "101" and "010": x=5 and y=2: 5 OR 2 = 7,    - "1010" and "10": x=10 and y=2: 10 OR 2 = 10,    - "10101" and "0": x=21 and y=0: 21 OR 0 = 21,    - "101010" and "": x=42 and y=0: 42 OR 0 = 42, - hence a(42) = 7. PROG (PARI) a(n) = my (v=oo, b=binary(n)); for (w=0, #b, v=min(v, bitor(fromdigits(b[1..w], 2), fromdigits(b[w+1..#b], 2)))); v CROSSREFS Cf. A327187 (x XOR y variant), A327188 (x AND y variant). Cf. A327189 (x + y variant), A327190 (x * y variant), A327191 (x - y variant). Cf. A327192 (max(x, y) variant), A327193 (min(x, y) variant). Cf. A327194 (x^2 + y^2 variant), A327195 (x^2 - y^2 variant). Sequence in context: A098505 A178395 A330958 * A021306 A214281 A125300 Adjacent sequences:  A327183 A327184 A327185 * A327187 A327188 A327189 KEYWORD nonn,look,base AUTHOR Rémy Sigrist, Aug 25 2019 STATUS approved

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Last modified January 22 12:55 EST 2022. Contains 350481 sequences. (Running on oeis4.)