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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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refs;
listen;
history;
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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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Table of n, a(n) for n=1..66.
Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A007949(a(n)))
Rémy Sigrist, PARI program for A298196
Index entries for sequences that are permutations of the natural numbers
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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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Cf. A007814, A007949, A304872 (inverse), A304881.
Sequence in context: A326776 A249746 A112480 * A112095 A260435 A255554
Adjacent sequences: A298193 A298194 A298195 * A298197 A298198 A298199
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KEYWORD
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nonn
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AUTHOR
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Rémy Sigrist, May 19 2018
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STATUS
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approved
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