A353623 a(n) is the least k > 0 such that n and k*n can be added without carries in balanced ternary.

1, 2, 3, 2, 2, 6, 3, 3, 2, 2, 2, 5, 2, 2, 6, 6, 5, 3, 3, 3, 3, 3, 6, 2, 2, 3, 2, 2, 2, 3, 2, 2, 9, 5, 12, 2, 2, 2, 12, 2, 2, 6, 6, 12, 11, 6, 6, 14, 5, 9, 8, 3, 3, 3, 3, 3, 3, 3, 9, 11, 3, 3, 3, 3, 3, 14, 6, 6, 2, 2, 9, 2, 2, 2, 3, 3, 6, 2, 2, 3, 2, 2, 2, 3, 2

Offset

0,2

Comments

Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Wikipedia, Balanced ternary

Formula

a(n) = A353624(n) / n for any n > 0.

a(3*n) = a(n).

Example

For n = 5:
- we consider the following cases:
      k  bter(k*5)  carries?
      -  ---------  --------
      1        1TT  yes
      2        101  yes
      3       1TT0  yes
      4       1T1T  yes
      5       10T1  yes
      6       1010  no
- so a(5) = 6.

Prog

(PARI) ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); return (1) }
a(n) = for (k=1, oo, if (ok(n, n*k), return (k)))

Crossrefs

Cf. A059095, A261891 (binary analog), A353624.

Sequence in context: A214320 A119809 A007653 * A272181 A154179 A300862

Adjacent sequences: A353620 A353621 A353622 * A353624 A353625 A353626

Keyword

nonn,base

Author

Rémy Sigrist, Apr 30 2022

Status

approved