A371263 The run lengths transform of the balanced ternary expansion of n corresponds to the run lengths transform of the binary expansion of a(n).

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

Offset

0,3

Comments

For any v > 0, the value v appears A225081(v-1) times in the sequence.

Links

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

Formula

abs(a(n+1) - a(n)) <= 1.

Example

The first terms, alongside the balanced ternary expansion of n and the binary expansion of a(n), are:
  n   a(n)  bter(n)  bin(a(n))
  --  ----  -------  ---------
   0     0        0          0
   1     1        1          1
   2     2       1T         10
   3     2       10         10
   4     3       11         11
   5     4      1TT        100
   6     5      1T0        101
   7     5      1T1        101
   8     5      10T        101
   9     4      100        100
  10     5      101        101
  11     6      11T        110
  12     6      110        110
  13     7      111        111
  14     8     1TTT       1000
  15     9     1TT0       1001

Prog

(PARI) a(n) = { my (r = [], d, l, v = 0); while (n, d = centerlift(Mod(n, 3)); l = 0; while (centerlift(Mod(n, 3))==d, n = (n-d)/3; l++; ); r = concat(l, r); ); for (k = 1, #r, v = (v+k%2)*2^r[k]-k%2); v }

Crossrefs

See A371256 for a similar sequence.

Cf. A225081, A371265.

Sequence in context: A342879 A342880 A337774 * A069928 A135585 A081094

Adjacent sequences: A371260 A371261 A371262 * A371264 A371265 A371266

Keyword

nonn,base

Author

Rémy Sigrist, Mar 16 2024

Status

approved