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Search: id:A140361
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| A140361 |
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tau(n), n >= 1, where tau(n) is equal to the number of additions, subtractions, or multiplications necessary to reach n starting from 1 and 2. |
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+0
2
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| 0, 0, 1, 1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 4, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 3, 4, 4, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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tau(n) is the name of the function given in the Coiran article, it has no relation to the divisor function. [From Leonid Broukhis (leob(AT)mailcom.com), Aug 04 2008]
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REFERENCES
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P. Coiran, Valiant's Model and the Cost of Computing Integers, Comput. Complex. 13 (2004), 131-146
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LINKS
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P. Coiran, http://perso.ens-lyon.fr/pascal.koiran/Publis/tau.springer.pdf.
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EXAMPLE
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tau(7) = 3 because we 7 = (2 + 1) + (2 * 2), or 7 = 2 * (2 + 2) - 1 and there is no shorter way.
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CROSSREFS
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Sequence in context: A084126 A135975 A136032 this_sequence A155940 A153095 A054483
Adjacent sequences: A140358 A140359 A140360 this_sequence A140362 A140363 A140364
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KEYWORD
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nonn
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AUTHOR
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Leonid Broukhis (leob(AT)mailcom.com), Jul 21 2008
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EXTENSIONS
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So this is tau( ) applied to which sequence? - N. J. A. Sloane (njas(AT)research.att.com), Jul 24 2008
Corrected, from 6 to 5, a(59) = ((2+2)*2)*8-1-4 and a(94) = (((2+2)+2)+4)*10-6 Leonid Broukhis (leob(AT)mailcom.com), Aug 04 2008
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