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Search: id:A115614
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| A115614 |
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Numbers n such that the smallest possible number of multiplications required to compute x^n is by 2 less than the number of multiplications obtained by Knuth's power tree method. |
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4
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| 8719, 17438, 28597, 34876, 54359, 56157, 57194, 57293, 59657, 60493, 67171, 69752, 71017, 71065, 75799, 78865, 100987, 108503, 108718, 110361, 112093, 112314, 112679, 113275, 114388, 114586, 115861, 119314, 119417, 120986, 133681, 133795
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence is based on a table of shortest addition chain lengths computed by N. Clift (neillclift(AT)msn.com), see link to A. Flammenkamp's web page given at A003313.
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EXAMPLE
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a(1)=8719 because this is the smallest number for which the addition chain produced by the power tree method [1 2 3 5 7 14 28 56 61 117 234 468 936 1872 3744 3861 7722 7783 8719] is by two terms longer than the shortest possible chains for this number. An example of such a chain is [1 2 3 6 9 15 17 34 68 136 272 544 1088 2176 4352 4367 8719].
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CROSSREFS
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Cf. A114622 [The power tree (as defined by Knuth)], A003313 [Length of shortest addition chain for n], A113945 [numbers such that Knuth's power tree method produces a result deficient by 1], A115615 [numbers such that Knuth's power tree method produces a result deficient by 3], A115616 [smallest number for which Knuth's power tree method produces an addition chain n terms longer than the shortest possible chain].
Sequence in context: A031877 A035909 A031852 this_sequence A165630 A067867 A110077
Adjacent sequences: A115611 A115612 A115613 this_sequence A115615 A115616 A115617
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org) and N. Clift (neillclift(AT)msn.com), Feb 15 2006
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