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A337224
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a(n) is the least number that can be obtained by replacing some repetitive part X^k in the binary expansion of n by X.
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3
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0, 1, 2, 1, 2, 5, 2, 1, 2, 5, 2, 5, 4, 5, 2, 1, 2, 5, 10, 9, 4, 5, 10, 5, 6, 9, 6, 11, 4, 5, 2, 1, 2, 5, 10, 11, 4, 9, 18, 9, 8, 9, 2, 11, 20, 5, 10, 5, 6, 13, 18, 19, 12, 13, 6, 13, 8, 9, 10, 11, 4, 5, 2, 1, 2, 5, 10, 11, 20, 17, 22, 17, 8, 9, 18, 19, 36, 37
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OFFSET
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0,3
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COMMENTS
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Leading zeros in binary expansions are ignored.
There are four fixed points: 0, 1, 2 and 5; their binary expansion is a squarefree string.
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LINKS
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FORMULA
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a(n) = 1 iff n = 2^k-1 for some k > 0.
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EXAMPLE
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The first terms, in decimal and in binary, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 2 10 10
3 1 11 1
4 2 100 10
5 5 101 101
6 2 110 10
7 1 111 1
8 2 1000 10
9 5 1001 101
10 2 1010 10
11 5 1011 101
12 4 1100 100
13 5 1101 101
14 2 1110 10
15 1 1111 1
16 2 10000 10
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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,base
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AUTHOR
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STATUS
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approved
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