A334374 Lexicographically earliest sequence of nonnegative integers such that for any distinct i and j, a(i) = a(j) implies that the Zeckendorf representations of i and of j have no common term.

0, 0, 0, 0, 1, 0, 2, 1, 0, 3, 2, 4, 5, 0, 4, 3, 2, 6, 5, 7, 8, 0, 8, 4, 3, 9, 6, 10, 11, 1, 12, 7, 13, 14, 0, 11, 5, 7, 15, 3, 13, 9, 6, 16, 10, 8, 17, 1, 18, 12, 19, 20, 14, 21, 22, 0, 19, 6, 10, 22, 4, 23, 15, 9, 24, 18, 11, 25, 13, 26, 16, 27, 28, 17, 29

Offset: 0

Author

Rémy Sigrist, Apr 25 2020

Keywords

• nonn

Comments

This sequence is a variant of A279125.

Examples

			The first terms, alongside their Zeckendorf representation in binary, are:
  n   a(n)  bin(A003714(a(n)))
  --  ----  ------------------
   0     0                   0
   1     0                   1
   2     0                  10
   3     0                 100
   4     1                 101
   5     0                1000
   6     2                1001
   7     1                1010
   8     0               10000
   9     3               10001
  10     2               10010
  11     4               10100
  12     5               10101
  13     0              100000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Wikipedia, Zeckendorf's theorem
• Rémy Sigrist, PARI program for A334374

Crossrefs

Cf. A000045, A279125.

Programs

PARI

See Links section.

Formula

a(n) = 0 iff n is a Fibonacci number (A000045).