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

Author

Rémy Sigrist, Apr 30 2022

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Wikipedia, Balanced ternary

Crossrefs

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

Programs

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)))

Formula

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

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