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

0,3

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.

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

Formula

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

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A231302 A231363 A225840 * A319409 A122543 A375421

Adjacent sequences: A361642 A361643 A361644 * A361646 A361647 A361648

Keyword

nonn,base

Author

Rémy Sigrist, Mar 19 2023

Status

approved