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?
