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

0,7

Comments

This sequence is a variant of A279125.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Wikipedia, Zeckendorf's theorem

Rémy Sigrist, PARI program for A334374

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A000045, A279125.

Sequence in context: A058604 A072661 A103432 * A103448 A186904 A216216

Adjacent sequences: A334371 A334372 A334373 * A334375 A334376 A334377

Keyword

nonn

Author

Rémy Sigrist, Apr 25 2020

Status

approved