A353624 a(0) = 0, and for n > 0, a(n) is the least multiple of n that can be added to n without carries in balanced ternary.

0, 2, 6, 6, 8, 30, 18, 21, 16, 18, 20, 55, 24, 26, 84, 90, 80, 51, 54, 57, 60, 63, 132, 46, 48, 75, 52, 54, 56, 87, 60, 62, 288, 165, 408, 70, 72, 74, 456, 78, 80, 246, 252, 516, 484, 270, 276, 658, 240, 441, 400, 153, 156, 159, 162, 165, 168, 171, 522, 649

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) = n * A353623(n).

a(3*n) = 3*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*5 = 30.

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 (n*k)))

Crossrefs

Cf. A059095, A261892 (binary analog), A353623.

Sequence in context: A230292 A082911 A005869 * A377998 A372610 A021978

Adjacent sequences: A353621 A353622 A353623 * A353625 A353626 A353627

Keyword

nonn,base

Author

Rémy Sigrist, Apr 30 2022

Status

approved