

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.


4



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
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OFFSET

1,1


COMMENTS

The sequence is based on a table of shortest addition chain lengths computed by Neill M. Clift, see link to Achim Flammenkamp's web page given at A003313.


LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..10000


EXAMPLE

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].


CROSSREFS

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: A233679 A266578 A031852 * A165630 A250999 A214171
Adjacent sequences: A115611 A115612 A115613 * A115615 A115616 A115617


KEYWORD

nonn


AUTHOR

Hugo Pfoertner and Neill M. Clift, Feb 15 2006


STATUS

approved



