OFFSET

0,4

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..9841

Wikipedia, Balanced ternary

EXAMPLE

For n = 7:

- the numbers k around 7, alongside their distance to 7, balanced ternary expansion and whether they require carries when added to 7, are:

k d bter(k) carries?

-- - ------- --------

3 4 10 no

4 3 11 yes

5 2 1TT yes

6 1 1T0 yes

7 0 1T1 yes

8 1 10T yes

9 2 100 yes

10 3 101 yes

11 4 11T yes

- so a(7) = 4.

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 (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d)))

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Apr 28 2022

STATUS

approved