A352501 a(n) is the distance from n to the nearest integer that can be added to n without carries in balanced ternary.

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

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=(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

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