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
Examples
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
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
Programs
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PARI
See Links section.
Comments