A331212 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and a(n+1) have no common 1 in their base phi representations.
0, 1, 2, 5, 3, 6, 4, 7, 12, 8, 13, 10, 16, 9, 14, 34, 11, 17, 30, 18, 31, 19, 32, 20, 33, 23, 36, 15, 35, 21, 37, 24, 39, 88, 22, 41, 25, 42, 26, 43, 27, 44, 81, 28, 45, 29, 46, 77, 47, 78, 48, 79, 49, 80, 52, 83, 50, 82, 51, 89, 40, 92, 38, 90, 53, 84, 59, 85
Offset: 0
Examples
The first terms, alongside their base phi representation, are: n a(n) phi(a(n)) -- ---- ------------- 0 0 0 1 1 1 2 2 10.01 3 5 1000.1001 4 3 100.01 5 6 1010.0001 6 4 101.01 7 7 10000.0001 8 12 100000.101001 9 8 10001.0001 10 13 100010.001001
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
- Rémy Sigrist, PARI program for A331212
- Wikipedia, Golden ratio base
Programs
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PARI
\\ See Links section.