A353158 a(n) is the distance from n to the nearest integer that can be added to n without carries in base 3.

0, 0, 1, 0, 0, 2, 3, 2, 1, 0, 0, 1, 0, 0, 2, 4, 6, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 0, 0, 2, 3, 2, 1, 0, 0, 1, 0, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4

Offset

0,6

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9841

Formula

a(n) = 0 iff n belongs to A005836.

Example

For n = 42:
- the numbers k around 42, alongside their distance to 42, ternary expansion and whether they require carries when added to 42, are:
      k   d  ter(k)  carries?
      --  -  ------  --------
      38  4    1102  no
      39  3    1110  yes
      40  2    1111  yes
      41  1    1112  yes
      42  0    1120  yes
      43  1    1121  yes
      44  2    1122  yes
      45  3    1200  yes
      46  4    1201  yes
- so a(42) = 4.

Prog

(PARI) ok(u, v) = sumdigits(u+v, 3)==sumdigits(u, 3)+sumdigits(v, 3)
a(n) = { for (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d))) }

Crossrefs

Cf. A005836 (positions of zeros), A167877, A353157 (binary variant).

Sequence in context: A017878 A301572 A017868 * A334476 A319573 A178904

Adjacent sequences: A353155 A353156 A353157 * A353159 A353160 A353161

Keyword

nonn,base

Author

Rémy Sigrist, Apr 27 2022

Status

approved