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

Author

Rémy Sigrist, Apr 27 2022

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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))) }

Formula

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