

A352501


a(n) is the distance from n to the nearest integer that can be added to n without carries in balanced ternary.


1



0, 1, 1, 2, 1, 1, 2, 4, 4, 5, 4, 4, 2, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 10, 11, 13, 13, 14, 13, 13, 11, 10, 13, 11, 10, 7, 5, 4, 4, 2, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 10, 11, 13, 13, 14, 16, 19, 20, 22, 28, 29, 31, 31, 32, 34, 37, 38, 40, 28, 29, 31, 31, 32
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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


FORMULA

a(n) = 1 iff n > 0 and n belongs to A003462 or A007051.
a(3*n) = 3*a(n)+1 for any n > 0.


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=(uuu)/3; v=(vvv)/3); return (1) }
a(n) = for (d=0, oo, if (ok(n, nd)  ok(n, n+d), return (d)))


CROSSREFS

Cf. A003462, A007051, A059095, A353158.
Sequence in context: A108746 A333270 A333272 * A119558 A333450 A210112
Adjacent sequences: A352498 A352499 A352500 * A352502 A352503 A352504


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Apr 28 2022


STATUS

approved



