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A090841
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Smallest prime whose product of digits is 7^n.
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6
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11, 7, 11177, 1777, 71777, 1777717, 1177717771, 77777177, 7177717777, 1777777777, 71777777777, 1717777777777, 7177777777777, 17777777777777, 17177777777777717, 7717777777777777, 1177777777177777777, 1777777777777777177, 7777177777777777777
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internal format)
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OFFSET
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0,1
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LINKS
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EXAMPLE
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a(6) = 1177717771 because its digital product is 7^6, and it is prime.
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MAPLE
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a:= proc(n) local k, t; for k from 0 do t:= min(select(isprime,
map(x-> parse(cat(x[])), combinat[permute]([1$k, 7$n]))));
if t<infinity then return t fi od
end:
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {18}]; p = 2; Do[q = Log[7, 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(8); a = Map[ FromDigits, Permutations[{1, 1, 7, 7, 7, 7, 7, 7, 7, 7}]]; Min[ Select[a, PrimeQ[ # ] &]]
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PROG
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(Python)
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations as mp
def a(n):
if n < 2: return [11, 7][n]
digits = n
while True:
for p in mp("1"*(digits-n) + "7"*n, digits):
t = int("".join(p))
if isprime(t): return t
digits += 1
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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