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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 (list; graph; refs; listen; history; text; internal format)
 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) LINKS David W. Wilson, Table of n, a(n) for n = 0..75 Dario A. Alpern, Factorization using the Elliptic Curve Method 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 Adjacent sequences: A205986 A205987 A205988 * A205990 A205991 A205992 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 02 2012 EXTENSIONS More terms from Alois P. Heinz, Feb 17 2012 STATUS approved

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Last modified March 3 13:27 EST 2024. Contains 370512 sequences. (Running on oeis4.)