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Search: id:A064818
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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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+0
2
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OFFSET
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1,2
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COMMENT
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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 (wasserma(AT)spawar.navy.mil), Aug 20 2002
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REFERENCES
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Bernardo Recaman Santos, Challenging Brainteasers, Sterling, NY, 2000.
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EXAMPLE
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24 = (2+sqrt(4))!. (Alternatively, 24 = sqrt((4!)^2) - David Johnson.)
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CROSSREFS
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Adjacent sequences: A064815 A064816 A064817 this_sequence A064819 A064820 A064821
Sequence in context: A132169 A072217 A052686 this_sequence A022374 A112660 A119066
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KEYWORD
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nonn,base,nice,more
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AUTHOR
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njas, Oct 23 2001
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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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