Search: id:A115614
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%I A115614
%S A115614 8719,17438,28597,34876,54359,56157,57194,57293,59657,60493,67171,69752,
%T A115614 71017,71065,75799,78865,100987,108503,108718,110361,112093,112314,
%U A115614 112679,113275,114388,114586,115861,119314,119417,120986,133681,133795
%N A115614 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.
%C A115614 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.
%e A115614 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].
%Y A115614 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].
%Y A115614 Sequence in context: A031877 A035909 A031852 this_sequence A165630 A067867 
               A110077
%Y A115614 Adjacent sequences: A115611 A115612 A115613 this_sequence A115615 A115616 
               A115617
%K A115614 nonn
%O A115614 1,1
%A A115614 Hugo Pfoertner (hugo(AT)pfoertner.org) and N. Clift (neillclift(AT)msn.com), 
               Feb 15 2006

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