A371256 The run lengths transform of the ternary expansion of n corresponds to the run lengths transform of the binary expansion of a(n).

0, 1, 1, 2, 3, 2, 2, 2, 3, 4, 5, 5, 6, 7, 6, 5, 5, 4, 4, 5, 5, 5, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 10, 10, 10, 11, 12, 13, 13, 14, 15, 14, 13, 13, 12, 11, 10, 10, 10, 11, 10, 9, 9, 8, 8, 9, 9, 10, 11, 10, 10, 10, 11, 11, 10, 10, 9, 8, 9, 10, 10, 11, 12, 13, 13

Offset: 0

Author

Rémy Sigrist, Mar 16 2024

Keywords

• nonn
• base
• easy

Comments

For any v >= 0, the value v appears 2^A005811(v) times in the sequence.

Examples

			The first terms, alongside the ternary expansion of n and the binary expansion of a(n), are:
  n   a(n)  ter(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     1       2          1
   3     2      10         10
   4     3      11         11
   5     2      12         10
   6     2      20         10
   7     2      21         10
   8     3      22         11
   9     4     100        100
  10     5     101        101
  11     5     102        101
  12     6     110        110
  13     7     111        111
  14     6     112        110
  15     5     120        101
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6561

Crossrefs

See A371263 for a similar sequence.

Cf. A004488, A005811, A005823, A005836, A101211, A166242, A371257.

Programs

PARI

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

Formula

a(A005823(n)) = n - 1.

a(A005836(n)) = n - 1.

a(A004488(n)) = a(n).

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