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

0,3

Comments

Leading zeros are ignored.

Every positive integers occurs infinitely many times.

Links

Table of n, a(n) for n=0..86.

Formula

a(n) <= A134021(n).

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

Example

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

Prog

(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); }

Crossrefs

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

Sequence in context: A194258 A165927 A127830 * A176816 A053284 A050371

Adjacent sequences: A371272 A371273 A371274 * A371276 A371277 A371278

Keyword

nonn,base,easy

Author

Rémy Sigrist, Mar 17 2024

Status

approved