login
A103822
Table of "minimum oddness" operation.
2
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
KEYWORD
base,easy,nonn,tabl
AUTHOR
Marc LeBrun, Feb 16 2005
STATUS
approved