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A344184
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Lexicographically earliest sequence of positive integers such that for any n > 0, the binary expansion of a(n) contains the binary expansion of k for k = 1..n and the binary expansion of a(n+1) is obtained by replacing a possibly empty substring of the binary expansion of a(n) by the binary expansion of n+1.
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1
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1, 2, 6, 12, 44, 44, 92, 184, 1208, 1336, 5304, 5304, 10680, 10680, 21368, 42736, 567024, 673520, 5383920, 5383920, 21535472, 172283632, 172283632, 172283632, 344774384, 344774384, 344774384, 344774384, 689559280, 689559280, 1379118576, 2758237152, 71477713888
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OFFSET
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1,2
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COMMENTS
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This sequence is a variant of A056744, easier to compute.
This sequence is not weakly increasing; a(109) < a(108).
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LINKS
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FORMULA
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EXAMPLE
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The first terms, alongside their binary expansion, are:
n a(n) bin(n) bin(a(n))
-- ----- ------ ---------------
1 1 1 1
2 2 10 10
3 6 11 110
4 12 100 1100
5 44 101 101100
6 44 110 101100
7 92 111 1011100
8 184 1000 10111000
9 1208 1001 10010111000
10 1336 1010 10100111000
11 5304 1011 1010010111000
12 5304 1100 1010010111000
13 10680 1101 10100110111000
14 10680 1110 10100110111000
15 21368 1111 101001101111000
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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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