A371275 a(n) is the number of runs in the balanced ternary expansion of n.

0, 1, 2, 2, 1, 2, 3, 3, 3, 2, 3, 2, 2, 1, 2, 3, 3, 4, 3, 4, 4, 4, 3, 3, 4, 4, 3, 2, 3, 4, 4, 3, 2, 3, 3, 3, 2, 3, 2, 2, 1, 2, 3, 3, 4, 3, 4, 4, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 4, 5, 5, 5, 4, 5, 4, 4, 3, 3, 4, 4, 5, 4, 5, 5, 5, 4, 3, 4, 4, 3, 2, 3, 4, 4, 3, 4

Offset: 0

Author

Rémy Sigrist, Mar 17 2024

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

Every positive integers occurs infinitely many times.

Examples

			The first terms, alongside the balanced ternary expansion of n, are:
  n    a(n)  bter(n)
  ---  ----  -------
    0     0        0
    1     1        1
    2     2       1T
    3     2       10
    4     1       11
    5     2      1TT
    6     3      1T0
    7     3      1T1
    8     3      10T
    9     2      100
   10     3      101
   11     2      11T
   12     2      110
   13     1      111
   14     2     1TTT
   15     3     1TT0
		

Crossrefs

Cf. A005811, A043555, A134021, A153773, A297770.

Programs

PARI

a(n) = { my (r = 0, d); while (n, r++; d = centerlift(Mod(n, 3)); while (d==centerlift(Mod(n, 3)), n = (n-d)/3;);); return (r); }

Formula

a(n) <= A134021(n).

a(A153773(k)) = k for any k > 0.