A103823 Table of "maximum oddness" operation.

0, 1, 1, 2, 1, 2, 3, 1, 1, 3, 4, 3, 2, 3, 4, 5, 1, 3, 3, 1, 5, 6, 5, 2, 3, 2, 5, 6, 7, 1, 5, 3, 3, 5, 1, 7, 8, 7, 6, 3, 4, 3, 6, 7, 8, 9, 1, 7, 3, 5, 5, 3, 7, 1, 9, 10, 9, 2, 7, 6, 5, 6, 7, 2, 9, 10, 11, 1, 9, 3, 7, 5, 5, 7, 3, 9, 1, 11, 12, 11, 10, 3, 4, 7, 6, 7, 4, 3, 10, 11, 12, 13, 1, 11, 3, 9, 5, 7, 7, 5

Offset

0,4

Comments

T(i,j) is whichever of i,j has the 1 in the rightmost differing bit of their binary representations. Defines a complete ordering of the integers: all odd numbers are "more odd" than all even 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

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) = max(Ri, Rj), where Rn is the reflection of n at the "binary point".

Example

T(11,13)=11, 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 (n), kk && !nn, return (k)))) } \\ Rémy Sigrist, Feb 08 2020

Crossrefs

Cf. A103822 (the complementary operation).

Sequence in context: A328902 A159335 A109004 * A355246 A136642 A080382

Adjacent sequences: A103820 A103821 A103822 * A103824 A103825 A103826

Keyword

base,easy,nonn,tabl

Author

Marc LeBrun, Feb 16 2005

Status

approved