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A298196
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Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the 2-adic valuation of a(n) equals the 3-adic valuation of a(n+1).
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3
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1, 2, 3, 4, 9, 5, 7, 8, 27, 10, 6, 12, 18, 15, 11, 13, 14, 21, 16, 81, 17, 19, 20, 36, 45, 22, 24, 54, 30, 33, 23, 25, 26, 39, 28, 63, 29, 31, 32, 243, 34, 42, 48, 162, 51, 35, 37, 38, 57, 40, 108, 72, 135, 41, 43, 44, 90, 60, 99, 46, 66, 69, 47, 49, 50, 75
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OFFSET
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1,2
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COMMENTS
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The 2-adic and 3-adic valuations of a number are respectively given by A007814 and by A007949.
For any distinct prime numbers p and q, let F_{p,q} be the lexicographically earliest sequence of distinct positive terms such that for any n > 0, the p-adic valuation of F_{p,q}(n) equals the q-adic valuation of F_{p,q}(n+1):
- in particular, F_{2,3} = a (this sequence) and F_{3,2} = A304881,
- the powers of q appear in order in F_{p,q},
- every power of q appear in F_{p,q},
- F_{p,q} is a permutation of the natural numbers.
This sequence is a permutation of the natural numbers, with inverse A304872.
The first known fixed points are: 1, 2, 3, 4, 7, 8, 10, 12, 42.
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LINKS
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EXAMPLE
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The first terms, alongside their 2-adic and 3-adic valuations, are:
n a(n) v2 v3
-- ---- -- --
1 1 0 0
2 2 1 0
3 3 0 1
4 4 2 0
5 9 0 2
6 5 0 0
7 7 0 0
8 8 3 0
9 27 0 3
10 10 1 0
11 6 1 1
12 12 2 1
13 18 1 2
14 15 0 1
15 11 0 0
16 13 0 0
17 14 1 0
18 21 0 1
19 16 4 0
20 81 0 4
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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