A361645 a(n) is the least k such that n appears in the k-th row of triangle A361644.

0, 1, 2, 2, 4, 5, 5, 4, 8, 9, 10, 10, 10, 10, 9, 8, 16, 17, 18, 18, 20, 21, 21, 20, 20, 21, 21, 20, 18, 18, 17, 16, 32, 33, 34, 34, 36, 37, 37, 36, 40, 41, 42, 42, 42, 42, 41, 40, 40, 41, 42, 42, 42, 42, 41, 40, 36, 37, 37, 36, 34, 34, 33, 32, 64, 65, 66, 66

Offset: 0

Author

Rémy Sigrist, Mar 19 2023

Keywords

• nonn
• base

Comments

All terms are fibbinary numbers (A003714).

To compute a(n): consider the run lengths in the binary expansion of n (i.e. the n-th row of A101211) and replace from left to right each value v > 1 at odd index with (1, v-1); at the end, there remain the run lengths in the binary expansion of a(n).

See A361676 for the greatest k's.

Examples

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2      10         10
   3     2      11         10
   4     4     100        100
   5     5     101        101
   6     5     110        101
   7     4     111        100
   8     8    1000       1000
   9     9    1001       1001
  10    10    1010       1010
  11    10    1011       1010
  12    10    1100       1010
  13    10    1101       1010
  14     9    1110       1001
  15     8    1111       1000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Rémy Sigrist, PARI program
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000975, A003714, A101211, A361645, A361676.

Programs

PARI

See Links section.

Formula

a(n) <= n with equality iff n is a fibbinary number (A003714).

a(n) <= A361676(n) with equality iff n belongs to A000975.