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%I #27 Jul 09 2023 11:49:34
%S 7,17,109,1019,10007,100019,1000171,10000019,100000007,1000000007,
%T 10000000019,100000000019,1000000000061,10000000000051,
%U 100000000000097,1000000000000091,10000000000000061,100000000000000019,1000000000000000177,10000000000000000051
%N a(n) = smallest prime >= 10^n with primitive root 10.
%C From _David W. Wilson_, Feb 17 2012 : (Start)
%C The decimal expansion of 1/a(n) includes every possible block of n digits. Conjecturally, a(n) is the smallest value with this property.
%C 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)
%H David W. Wilson, <a href="/A205989/b205989.txt">Table of n, a(n) for n = 0..75</a>
%H Dario A. Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>
%p with(numtheory):
%p a:= proc(n) local p;
%p p:= nextprime(10^n);
%p while 1 in map(q-> 10 &^ ((p-1)/q) mod p, factorset(p-1)) or
%p 1 <> (10 &^ (p-1) mod p)
%p do p:= nextprime(p) od; p
%p end:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 17 2012
%t 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 *)
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Feb 02 2012
%E More terms from _Alois P. Heinz_, Feb 17 2012
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