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A129523
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Numbers of the form 2^j +- 2^i for 0 <= i < j, in ascending order.
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2
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 24, 28, 30, 31, 32, 33, 34, 36, 40, 48, 56, 60, 62, 63, 64, 65, 66, 68, 72, 80, 96, 112, 120, 124, 126, 127, 128, 129, 130, 132, 136, 144, 160, 192, 224, 240, 248, 252, 254, 255, 256, 257, 258, 260, 264, 272
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OFFSET
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1,2
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COMMENTS
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Positive sums and differences of pairs of distinct powers of two, sorted, with duplicates removed.
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LINKS
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FORMULA
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x(n) = { 2^x - 2^y if x < y }, { 2^x if x = y }, { 2^x + 2^y if x > y} where x = ceiling(sqrt(n)) and y = n - (x-1)^2 - 1.
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EXAMPLE
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1 = 2^1 - 2^0; 2 = 2^2 - 2^1; 3 = 2^1 + 2^0 or 2^2 - 2^0; 4 = 2^3 - 2^2; 5 = 2^2 + 2^0.
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MATHEMATICA
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Union[Flatten[Table[{2^n, 2^n - 2^k, 2^n + 2^k}, {n, 8}, {k, 0, n - 1}]]] (* Ivan Neretin, Jul 29 2015 *)
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PROG
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(Octave) x=[]; m=12; for i = 0:m; x=[x, 2^i-2.^([(i-2):-1:0]), 2^i, 2^i+2.^([0 :(i-2)])]; end; x
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Phil Rutschman (phil(AT)rsnsoft.com), Apr 19 2007
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STATUS
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approved
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