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A353623
a(n) is the least k > 0 such that n and k*n can be added without carries in balanced ternary.
3
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
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 30 2022
STATUS
approved