A088653 Smallest prime whose product of digits is 3^n.

11, 3, 19, 139, 199, 1399, 1999, 13999, 99991, 139999, 199999, 1399999, 9999991, 19399999, 19999999, 919999939, 1399939999, 1999993999, 9199999999, 19399999999, 99999199999, 199999939999, 991999999999, 1999399999999

Offset: 0

Author

Robert G. Wilson v, Nov 22 2003

Keywords

• base
• nonn

Examples

			a(5) = 1399 and the digital product is 3^5.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A089365, A090840, A091465, A090841, A089298.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; a = Table[0, {18}]; p = 2; Do[q = Log[3, Times @@ IntegerDigits[p]]; If[q != 0 && IntegerQ[q] && a[[q]] == 0, a[[q]] = p; Print[q, " = ", p]]; p = NextPrim[p], {n, 1, 10^9}]
For a(23): a = Map[ FromDigits, Join[{0}, # ] & /@ Permutations[{1, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 }]]; Min[ Select[a, PrimeQ[ # ] & ]]
For a(11): a = Map[ FromDigits, Permutations[{2, 6, 8, 8, 8, 9, 9, 9, 9, 9}]]; Min[ Select[a, PrimeQ[ # ] & ]]