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Interesting Smooth numbers

Posted 10 years ago
At reddit, there is a problem to find a permutation of 123456789 which has highest prime factor 7.  That's the same as a 7-smooth number. 619573248 is a 7-smooth number, and it's easy to find the other. 11859210 and 11859211 consecutive 19-smooth numbers.

I decided to find some smooth numbers consisting of 2 digits. 292229292292 is 29-smooth.

 pairs = Select[Tuples[Range[9], {2}], Length[Union[#]] == 2 &];
 Monitor[Sort[
   Flatten[Table[
     Take[Sort[
       Table[{First[
          Last[FactorInteger[
            FromDigits[
             IntegerDigits[n, 2] /. Thread[{0, 1} -> pairs[[gg]]]]]]],
         n, FromDigits[
         IntegerDigits[n, 2] /. Thread[{0, 1} -> pairs[[gg]]]]}, {n,
        513, 20000}]], 10], {gg, 1, 72}], 1]], gg]


Here are some others:
{{23, 615, 4334433444}, {23, 615, 8668866888}, {23, 927, 8889988888}, {23, 975, 4444994444}, {29, 2989, 292229292292},
{37,  2394, 455454544545}, {37, 2583, 545444454555}, {37, 2772,  454544545455}, {37, 3087, 554444445555}, {37, 3087,  556666665555}, {37, 3591, 111333333111}, {37, 3591,  222666666222}, {37, 3591, 333999999333}, {37, 3906,  777727222272}, {37, 3969, 555554444445}, {41, 3906,  777737333373}, {43, 2142, 722227277772}, {43, 4032, 111111888888}

Are there any really interesting smooth numbers in bigger examples?
POSTED BY: Ed Pegg
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