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A316994
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Lexicographically earliest sequence of distinct positive terms such that a(1) = 2 and for any n > 0 the binary representation of a(n) appears as a substring in the binary representation of Sum_{k=1..n} a(k).
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1
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2, 1, 3, 5, 10, 4, 8, 11, 6, 7, 18, 24, 14, 16, 42, 43, 12, 13, 15, 36, 9, 19, 20, 17, 23, 25, 21, 28, 22, 26, 33, 35, 37, 29, 40, 34, 27, 30, 50, 46, 31, 41, 54, 65, 70, 32, 76, 39, 81, 69, 45, 47, 48, 103, 53, 51, 49, 52, 56, 55, 57, 135, 121, 73, 59, 38, 58
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OFFSET
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1,1
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COMMENTS
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This sequence is a variant of A316993.
This sequence is conjectured to be infinite.
This sequence is conjectured to be a permutation of the natural numbers.
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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} a(k), are:
n a(n) bin(a(n)) bin(Sum_{k=1..n} a(k))
-- ---- --------- ----------------------
1 2 10 10
2 1 1 11
3 3 11 110
4 5 101 1011
5 10 1010 10101
6 4 100 11001
7 8 1000 100001
8 11 1011 101100
9 6 110 110010
10 7 111 111001
11 18 10010 1001011
12 24 11000 1100011
13 14 1110 1110001
14 16 10000 10000001
15 42 101010 10101011
16 43 101011 11010110
17 12 1100 11100010
18 13 1101 11101111
19 15 1111 11111110
20 36 100100 100100010
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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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