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