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

Author

Rémy Sigrist, Mar 16 2024

Keywords

• nonn
• base

Comments

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

Examples

			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
		

Links

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

Crossrefs

See A371256 for a similar sequence.

Cf. A225081, A371265.

Programs

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 }

Formula

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