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A317788
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Lexicographically earliest infinite sequence of distinct positive terms such that for any n > 1, the binary representation of a(n) appears as a substring in the binary representation of Sum_{k=1..n-1} a(k).
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2
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2, 1, 3, 6, 4, 8, 12, 9, 5, 18, 17, 10, 7, 19, 14, 16, 11, 20, 13, 24, 22, 15, 32, 36, 34, 25, 23, 37, 27, 21, 26, 64, 69, 40, 43, 29, 30, 35, 39, 44, 28, 42, 53, 129, 72, 38, 31, 81, 45, 50, 46, 47, 49, 74, 41, 54, 55, 51, 52, 57, 58, 128, 68, 70, 140, 77, 60
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OFFSET
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1,1
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COMMENTS
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The sequence must start with a(1) = 2 in order to be infinite, and for any n > 1, a(n) <= Sum_{k=1..n-1} a(k).
This sequence has similarities with A160855.
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LINKS
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EXAMPLE
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The first terms, alongside the binary representations of a(n) and of Sum_{k=1..n-1} a(k), are:
n a(n) bin(a(n)) bin(Sum_{k=1..n-1} a(k))
-- ---- --------- ------------------------
1 2 10 0
2 1 1 10
3 3 11 11
4 6 110 110
5 4 100 1100
6 8 1000 10000
7 12 1100 11000
8 9 1001 100100
9 5 101 101101
10 18 10010 110010
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PROG
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(C++) 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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