For base 26, 5 digits works, and the result of 400 @ 28561 agrees with Hans's numbers. Base 27, two digits suffice, result of 234 using 3. Base 28, three digits, high is 432 using 49. I need to make my program smarter at this point. On Fri, Dec 16, 2011 at 10:27 AM, Michael Kleber <michael.kleber@gmail.com> wrote:
I can confirm that Hans's numbers below through k=25 are correct, by using the check-the-last-d-digits trick that Tom Rokicki pointed out yesterday.
For bases 4, 8, 9, 16, 25 it suffices to check the bottom 2 digits. For bases 6, 12, 15, 20, 21, 24 it suffices to check the bottom 3 digits. For bases 10, 14 it suffices to check the bottom 4 digits. For bases 18, 22 it suffices to check the bottom 5 digits.
(Base 26 is working through 5-digit suffixes now.)
--Michael
On Thu, Dec 15, 2011 at 7:22 PM, Hans Havermann <gladhobo@teksavvy.com>wrote:
Tom Rokicki:
Okay, different bases.
I ran this earlier just by checking all x up to a million in the given base. If a million is high enough, then the k's are good...
base {x,k}
04 {2,6} 06 {9,20} 08 {2,28} 09 {3,24} 10 {125,72} 12 {16,99} 14 {343,104} 15 {25,126} 16 {2,120} 18 {6561,272} 20 {25,304} 21 {49,180} 22 {14641,336} 24 {32,414} 25 {5,120} 26 {28561,400} 27 {3,234} 28 {49,432} 30 {1000,783} 32 {2,496} 33 {1331,864} 34 {2,561} 35 {49,850} 36 {1458,1120} 38 {2,703} 39 {2197,1026} 40 {50,1248} 42 {49,1476} 44 {2662,1376} 45 {75,1188} 46 {2,1035} 48 {64,1692} 49 {7,336} 50 {3125,1960} 51 {4913,1350} 52 {4394,1632} 54 {177147,2544} 55 {121,1350} 56 {64,2695} 57 {6859,1512} 58 {2,1653} 60 {4000,3186} 62 {2,1891} 63 {81,3038} 64 {2,2016} 65 {169,1600} 66 {5324,3510} 68 {4913,4288} 69 {12167,1836} 70 {6125,3864} 72 {81,4544} 74 {2,2701} 75 {125,3330}
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