1,1

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. Known further terms for this sequence are 25747725, 26429018, 26640937, but the check for smaller terms after a(4) is not completed.

a(1)=6475341 because this is the smallest number for which the addition chain produced by the power tree method [1 2 3 5 7 14 19 38 76 79 158 316 632 1264 2528 5056 5063 10119 12647 25294 50588 101176 202352 404704 809408 809427 1618835 3237670 6475340 6475341] is by three terms longer than the shortest possible chains for this number. An example of such a chain is [1 2 4 8 16 32 64 65 129 258 387 774 1548 1613 3161 6322 12644 25288 50576 101152 202304 404608 809216 1618432 3236864 3238477 6475341].

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], A115614 [numbers such that Knuth's power tree method produces a result deficient by 2], 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: A138941 A018895 A141594 this_sequence A022237 A116173 A088238

Adjacent sequences: A115612 A115613 A115614 this_sequence A115616 A115617 A115618

hard,more,nonn

Hugo Pfoertner (hugo(AT)pfoertner.org) and N. Clift (neillclift(AT)msn.com), Feb 15 2006