A353157 a(n) is the distance from n to the nearest integer whose binary expansion has no common 1-bits with that of n.

0, 1, 1, 1, 1, 3, 2, 1, 1, 3, 5, 5, 4, 3, 2, 1, 1, 3, 5, 7, 9, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

Offset

0,6

Comments

Equivalently the distance to the nearest integer that can be added without carries in base 2.

Links

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

Index entries for sequences related to binary expansion of n

Formula

a(n) = min(A006257(n), A080079(n)) for any n > 0.

a(n) = 1 iff n belongs to A097110.

a(n) = n/2 iff n belongs to A020988.

a(n) = n/4 iff n belongs to A108019.

2*a(n) - a(2*n) = 0 or 1.

Example

For n = 42 ("101010" in binary):
- 21 ("10101") is the greatest number <= 42 that has no common 1-bits with 42,
- 128 ("1000000") is the least number >= 42 that has no common 1-bits with 42,
- so a(42) = min(42-21, 128-42) = min(21, 86) = 21.

Prog

(PARI) a(n) = { my (high=2^#binary(n), low=high-1-n); min(n-low, high-n) }

Crossrefs

Cf. A006257, A020988, A097110, A080079, A108019, A353158.

Sequence in context: A152176 A152175 A321620 * A134520 A188316 A197027

Adjacent sequences: A353154 A353155 A353156 * A353158 A353159 A353160

Keyword

nonn,base

Author

Rémy Sigrist, Apr 27 2022

Status

approved