A330984 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) have no common 1 in their base phi representations.

0, 2, 1, 5, 6, 3, 4, 12, 13, 14, 16, 17, 7, 8, 9, 34, 10, 11, 30, 31, 32, 35, 36, 33, 37, 41, 42, 43, 45, 46, 18, 19, 20, 23, 15, 21, 22, 24, 88, 89, 92, 25, 26, 27, 81, 28, 29, 77, 78, 79, 82, 83, 80, 84, 90, 93, 91, 94, 106, 85, 86, 95, 96, 87, 97, 107, 108

Offset

0,2

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Links

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

Rémy Sigrist, Scatterplot of (x, y) such that x and y have no common 1 in their base phi representations and 0 <= x, y <= 1000

Rémy Sigrist, PARI program for A330984

Wikipedia, Golden ratio base

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the base phi representations of n and of a(n), are:
  n   a(n)  phi(n)      phi(a(n))
  --  ----  ----------  -------------
   0     0      0            0
   1     2      1           10.01
   2     1     10.01         1
   3     5    100.01      1000.1001
   4     6    101.01      1010.0001
   5     3   1000.1001     100.01
   6     4   1010.0001     101.01
   7    12  10000.0001  100000.101001
   8    13  10001.0001  100010.001001
   9    14  10010.0101  100100.001001
  10    16  10100.0101  101000.100001

Prog

(PARI) See Links section.

Crossrefs

Cf. A238757 (binary analog), A331212.

Sequence in context: A067311 A341487 A162750 * A353648 A075680 A192024

Adjacent sequences: A330981 A330982 A330983 * A330985 A330986 A330987

Keyword

nonn,base

Author

Rémy Sigrist, Apr 23 2020

Status

approved