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A088653 Smallest prime whose product of digits is 3^n. 6
11, 3, 19, 139, 199, 1399, 1999, 13999, 99991, 139999, 199999, 1399999, 9999991, 19399999, 19999999, 919999939, 1399939999, 1999993999, 9199999999, 19399999999, 99999199999, 199999939999, 991999999999, 1999399999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

EXAMPLE

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

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[ # ] & ]]

CROSSREFS

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

Sequence in context: A110434 A110798 A329293 * A317311 A107598 A087100

Adjacent sequences:  A088650 A088651 A088652 * A088654 A088655 A088656

KEYWORD

base,nonn

AUTHOR

Robert G. Wilson v, Nov 22 2003

STATUS

approved

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Last modified June 17 17:32 EDT 2021. Contains 345085 sequences. (Running on oeis4.)