login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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