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A064818
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Exotic numbers: write n in base 10 as d_1 d_2 ... d_k; sequence gives numbers n which can be obtained by using the digits d_1 ... d_k exactly once, at most one each of the symbols +, -, x, "divided by", sqrt, factorial, ^, together with any number of parentheses.
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3
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OFFSET
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1,2
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COMMENTS
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The trivial representation n = d_1 d_2 ... d_k is excluded.
I've found some more terms: 36 = 3!*6, 64 = sqrt(4)^6, 125 = 5^(1+2), 216 = 6^(1+2). But I haven't done an exhaustive search, so I'm not sure what a(5) is. There could be a term between 25 and 36. - David Wasserman, Aug 20 2002
From D. S. McNeil, Sep 07 2010: Probably the sequence up to 1000 is [1, 2, 24, 25, 36, 64, 71, 120, 121, 125, 126, 127, 128, 153, 184, 216, 289, 324, 337, 343, 347, 354, 355, 360, 384, 456, 464, 624, 625, 648, 660, 688, 693, 720, 729, 736], with about 10% chance of error.
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REFERENCES
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Bernardo Recamán Santos, Challenging Brainteasers, Sterling, NY, 2000.
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LINKS
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EXAMPLE
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24 = (2+sqrt(4))!.
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CROSSREFS
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KEYWORD
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nonn,base,nice,more
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AUTHOR
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EXTENSIONS
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The reference also gives 121 = 11^2, 127 = 2^7 - 1, 128 = 2^(8-1), 144 = (1+4)! + 4!, but missed 120 = (10/2)! found by Peter Shor.
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STATUS
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approved
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