A103822 Table of "minimum oddness" operation.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 2, 1, 0, 0, 4, 2, 2, 4, 0, 0, 1, 4, 3, 4, 1, 0, 0, 6, 2, 4, 4, 2, 6, 0, 0, 1, 2, 5, 4, 5, 2, 1, 0, 0, 8, 2, 6, 4, 4, 6, 2, 8, 0, 0, 1, 8, 3, 4, 5, 4, 3, 8, 1, 0, 0, 10, 2, 8, 4, 6, 6, 4, 8, 2, 10, 0, 0, 1, 2, 9, 8, 5, 6, 5, 8, 9, 2, 1, 0, 0, 12, 2, 10, 4, 8, 6, 6, 8, 4, 10, 2

Offset

0,8

Comments

T(i,j) is whichever of i,j has the 0 in the rightmost differing bit of their binary representations. Defines a complete ordering of the integers: all even numbers are "less odd" than all odd numbers, for numbers of same parity remaining bits are recursively compared to determine ordering.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10295 (antidiagonals 0..142)

Rémy Sigrist, Colored representation of T(n, k) for n, k = 0..1023 (where the hue is function of T(n, k))

Formula

T(i, j) = min(Ri, Rj), where Rn is the reflection of n at the "binary point".

Example

T(11,13)=13, since the rightmost differing bit position is 1 for 11=1011 binary and 0 for 13=1101 binary.

Prog

(PARI) T(n, k) = { if (n==k, return (n), for (i=0, oo, my (nn=bittest(n, i), kk=bittest(k, i)); if (nn && !kk, return (k), kk && !nn, return (n)))) } \\ Rémy Sigrist, Feb 08 2020

Crossrefs

Cf. A103823 (the complementary operation).

Sequence in context: A328800 A328802 A355245 * A225927 A029392 A035379

Adjacent sequences: A103819 A103820 A103821 * A103823 A103824 A103825

Keyword

base,easy,nonn,tabl

Author

Marc LeBrun, Feb 16 2005

Status

approved