A361676 a(n) is the greatest k such that n appears in the k-th row of triangle A361644.

0, 1, 2, 3, 5, 5, 6, 7, 11, 10, 10, 11, 13, 13, 14, 15, 23, 22, 21, 21, 21, 21, 22, 23, 27, 26, 26, 27, 29, 29, 30, 31, 47, 46, 45, 45, 43, 42, 42, 43, 43, 42, 42, 43, 45, 45, 46, 47, 55, 54, 53, 53, 53, 53, 54, 55, 59, 58, 58, 59, 61, 61, 62, 63, 95, 94, 93

Offset: 0

Author

Rémy Sigrist, Mar 20 2023

Keywords

• nonn
• base

Comments

All terms belong to A003754.

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 even index with (1, v-1); at the end, there remain the run lengths in the binary expansion of a(n).

See A361645 for the least 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     3      11         11
   4     5     100        101
   5     5     101        101
   6     6     110        110
   7     7     111        111
   8    11    1000       1011
   9    10    1001       1010
  10    10    1010       1010
  11    11    1011       1011
  12    13    1100       1101
  13    13    1101       1101
  14    14    1110       1110
  15    15    1111       1111
		

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, A003754, A101211, A361644, A361645.

Programs

PARI

See Links section.

Formula

a(n) >= n with equality iff n belongs to A003754.

a(n) >= A361645(n) with equality iff n belongs to A000975.