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Search: id:A078405
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| A078405 |
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Smallest positive integer than cannot be obtained from exactly n copies of n using parentheses and the operations +, -, /, *, ^ and concatenation. |
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+0
2
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OFFSET
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1,1
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COMMENT
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Only the original numbers may be concatenated, not the results of arithmetic operations (but see A078413).
Comments from Max Alekseyev (maxale(AT)gmail.com), Apr 17 2005: Sequence is infinite. There are a finite number of expressions including n copies of n and various arithmetic operations. Hence A078405(n) is defined for any n. There is a trivial upper bound: A078405(n) < (n-1)! * 6^(n-1).
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LINKS
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Erich Friedman, Title? (Possible inspiration for this sequence)
Index entries for similar sequences
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EXAMPLE
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With three 3's one can form 1=(3/3)^3, 2=3-3/3, 3=3+3-3, 4=3+3/3, but not 5, so a(3)=5.
With four 4's one can get 1=44/44, 2=4/4+4/4, 3=4-(4/4)^4, 4=4+(4-4)^4, 5=4+(4/4)^4, 6=(4+4)/4+4, 7=44/4-4, 8=4+4+4-4, 9=4+4+4/4, 10=(44-4)/4, but not 11, so a(4)=11.
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CROSSREFS
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Cf. A078413.
Sequence in context: A117400 A005637 A104080 this_sequence A109278 A112527 A049680
Adjacent sequences: A078402 A078403 A078404 this_sequence A078406 A078407 A078408
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KEYWORD
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nonn,base
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AUTHOR
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Kit Vongmahadlek (kit119(AT)yahoo.com), Dec 27 2002
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EXTENSIONS
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a(7), a(8) and a(9) computed by Joseph DeVincentis (devjoe(AT)yahoo.com), Dec 27 2002
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