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A205989
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a(n) = smallest prime >= 10^n with primitive root 10.
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1
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7, 17, 109, 1019, 10007, 100019, 1000171, 10000019, 100000007, 1000000007, 10000000019, 100000000019, 1000000000061, 10000000000051, 100000000000097, 1000000000000091, 10000000000000061, 100000000000000019, 1000000000000000177, 10000000000000000051
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OFFSET
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0,1
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COMMENTS
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From David W. Wilson, Feb 17 2012 : (Start)
The decimal expansion of 1/a(n) includes every possible block of n digits. Conjecturally, a(n) is the smallest value with this property.
If Artin's conjecture is true, there are an infinite number of primes with primitive root 10, which implies that a(n) exists for all n. Artin's conjecture remains open. (End)
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LINKS
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David W. Wilson, Table of n, a(n) for n = 0..75
Computational assistance
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MAPLE
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with(numtheory):
a:= proc(n) local p;
p:= nextprime(10^n);
while 1 in map(q-> 10 &^ ((p-1)/q) mod p, factorset(p-1)) or
1 <> (10 &^ (p-1) mod p)
do p:= nextprime(p) od; p
end:
seq(a(n), n=0..20); # Alois P. Heinz, Feb 17 2012
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MATHEMATICA
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spr10[n_]:=Module[{p=NextPrime[n]}, While[PrimitiveRoot[p, 10]!=10, p = NextPrime[ p]]; p]; Join[{7, 17}, Table[spr10[10^d], {d, 2, 20}]] (* Harvey P. Dale, Nov 18 2020 *)
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CROSSREFS
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Sequence in context: A284209 A068172 A067185 * A262474 A284416 A063384
Adjacent sequences: A205986 A205987 A205988 * A205990 A205991 A205992
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Feb 02 2012
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EXTENSIONS
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More terms from Alois P. Heinz, Feb 17 2012
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STATUS
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approved
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