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A112388
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a(n) is the smallest prime p such that p^n contains every digit.
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2
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10123457689, 101723, 5437, 2339, 1009, 257, 139, 173, 83, 67, 31, 29, 37, 17, 17, 47, 19, 7, 5, 23, 23, 5, 11, 11, 17, 5, 5, 5, 5, 11, 5, 11, 11, 5, 5, 7, 5, 7, 3, 5, 5, 7, 7, 7, 3, 7, 3, 3, 5, 5, 5, 5, 3, 7, 7, 5, 3, 7, 5, 3, 3, 3, 3, 3, 3, 5, 3, 2, 3, 2, 3, 3, 3, 3, 5, 3, 3, 3, 2, 3, 5, 2
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n)=2 for all n>168. Checked up to n = 20000. - Robert Israel, Aug 28 2020
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LINKS
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MAPLE
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f:= proc(n) local k;
k:= 1:
do k:= nextprime(k);
if convert(convert(k^n, base, 10), set) = {$0..9} then return k fi
od
end proc:
f(1):= 10123457689:
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[ Union@IntegerDigits[ Prime[k]^n] != {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, k++ ]; Prime[k]]; Array[f, 82] (* Robert G. Wilson v, Dec 06 2005 *)
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PROG
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(Python)
from sympy import nextprime
def a(n):
if n == 1: return 10123457689
p = 2
while not(len(set(str(p**n))) == 10): p = nextprime(p)
return p
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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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