A377738 a(n) is the least m > n such that the Zeckendorf representations of m and n have the same number of terms.

2, 3, 5, 6, 8, 7, 9, 13, 10, 11, 14, 17, 21, 15, 16, 18, 19, 22, 20, 25, 34, 23, 24, 26, 27, 29, 28, 30, 35, 31, 32, 38, 46, 55, 36, 37, 39, 40, 42, 41, 43, 47, 44, 45, 48, 51, 56, 49, 50, 52, 53, 59, 54, 67, 89, 57, 58, 60, 61, 63, 62, 64, 68, 65, 66, 69, 72

Offset

1,1

Comments

A permutation of the numbers missing from A027941.

To compute a(n):

- in the Zeckendorf representation of n,

- locate the rightmost term A000045(k) such that A000045(k+2) is not a term,

- replace A000045(k) by A000045(k+1),

- replace the c terms < A000045(k) by A027941(c).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Index entries for sequences related to Zeckendorf expansion of n

Formula

a(A000045(k)) = A000045(k+1) for any k >= 2.

Example

The first terms, alongside their Zeckendorf representations, are:
  n   a(n)  A014417(n)  A014417(a(n))
  --  ----  ----------  -------------
   1     2           1             10
   2     3          10            100
   3     5         100           1000
   4     6         101           1001
   5     8        1000          10000
   6     7        1001           1010
   7     9        1010          10001
   8    13       10000         100000
   9    10       10001          10010
  10    11       10010          10100
  11    14       10100         100001
  12    17       10101         100101
  13    21      100000        1000000
  14    15      100001         100010

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A000045, A003714, A007895, A014417, A027941, A057168, A228915.

Sequence in context: A269670 A333480 A373600 * A036587 A075145 A086142

Adjacent sequences: A377735 A377736 A377737 * A377739 A377740 A377741

Keyword

nonn,base

Author

Rémy Sigrist, Nov 05 2024

Status

approved