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A205989
a(n) = smallest prime >= 10^n with primitive root 10.
1
7, 17, 109, 1019, 10007, 100019, 1000171, 10000019, 100000007, 1000000007, 10000000019, 100000000019, 1000000000061, 10000000000051, 100000000000097, 1000000000000091, 10000000000000061, 100000000000000019, 1000000000000000177, 10000000000000000051
OFFSET
0,1
COMMENTS
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)
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A284209 A068172 A067185 * A262474 A284416 A063384
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 02 2012
EXTENSIONS
More terms from Alois P. Heinz, Feb 17 2012
STATUS
approved