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A364201
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Lexicographically earliest sequence of distinct positive integers such that the sum of all terms a(1)..a(n) in binary is a substring of the concatenation of all terms a(1)..a(n) in binary.
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1
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1, 2, 3, 5, 11, 7, 16, 9, 6, 18, 4, 13, 10, 15, 12, 23, 20, 8, 27, 19, 36, 26, 22, 17, 21, 31, 25, 14, 29, 28, 30, 57, 24, 32, 39, 43, 40, 34, 38, 46, 33, 35, 42, 37, 55, 44, 58, 48, 56, 52, 41, 45, 64, 63, 54, 61, 60, 49, 50, 51, 65, 47, 67, 88, 132, 73, 76, 68, 109, 59, 82, 87, 62, 98, 69, 70
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OFFSET
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1,2
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COMMENTS
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In the first 10000 terms the smallest number that has not yet appeared is 7026; it is conjectured all numbers eventually appear.
The fixed points begin 1, 2, 3, 29, 48, 68, 96, 182, 471, 839, ... . It is likely there are infinitely more.
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LINKS
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EXAMPLE
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a(2) = 2 as a(1) + 2 = 1 + 2 = 3 = 11_2, which is a substring of "a(1)"_2 + "2"_2 = "1" + "10" = "110".
a(4) = 5 as a(1) + a(2) + a(3) + 5 = 1 + 2 + 3 + 5 = 11 = 1011_2, which is a substring "a(1)"_2 + "a(2)"_2 + "a(3)"_2 + "5"_2 = "1" + "10" + "11" + "101" = "11011101".
a(5) = 11 as a(1) + a(2) + a(3) + a(4) + 11 = 1 + 2 + 3 + 5 + 11 = 22 = 10110_2, which is a substring "a(1)"_2 + "a(2)"_2 + "a(3)"_2 + "a(4)"_2 + "11"_2 = "1" + "10" + "11" + "101" + "1011" = "110111011011".
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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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