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1, 2, 3, 4, 6, 8, 11, 15, 20, 27, 36, 48, 64, 85, 116, 153, 208, 273, 366, 493, 649, 888, 1161, 1579, 2092, 2784, 3783, 4946, 6772, 8875, 11977, 16065, 21193, 28979, 37823, 51633, 68117, 91045, 123377, 161622, 221441, 289493, 392259, 523328, 692771, 945393
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Let U(n,j) be the j-th smallest missing number in A119435(1..n-1). Example: for A119435(1..11), U(12,j) begins {6, 8, 10, 11, 14, ...}. Therefore we may alternatively define A119435(n) = U(n, A030101(n)).
Theorem: A119435(2^k) represents a local minimum. Proof: Observe that A030101(2^k) = 1. 2^k expressed in binary is 1 followed by zeros. When we reverse this number, the leading zeros are trivial and we read the number 1 in the 2^0 place. Therefore we select U(2^k, 1), which is the smallest missing number in A119435(1..n-1). Hence, a(n) = A119435(2^n).
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LINKS
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MATHEMATICA
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a = {1}; nn = 2^14; Do[AppendTo[a, Complement[Range[i + 2 nn], a][[IntegerReverse[i, 2]] ]], {i, 2, nn}]; Array[a[[2^#]] &, Floor@ Log2@ Length@ a - 1, 0]]
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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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EXTENSIONS
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STATUS
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approved
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