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A060503 Primes p that have a primitive root between 0 and p that is not a primitive root of p^2. 8


%S 2,29,37,43,71,103,109,113,131,181,191,211,257,263,269,283,349,353,

%T 359,367,373,397,439,449,461,487,509,563,599,617,619,631,641,647,653,

%U 701,739,743,773,797,839,857,863,883,887,907,919,947,971,983,1019,1031

%N Primes p that have a primitive root between 0 and p that is not a primitive root of p^2.

%C The smallest primitive roots of p that is not a primitive root of p^2 are in A060504.

%C Except for the initial term 2, this is a subset of A134307. - _Jeppe Stig Nielsen_, Jul 31 2015

%H Robert Israel, <a href="/A060503/b060503.txt">Table of n, a(n) for n = 1..1000</a>

%F filter:= proc(p) local x;

%F if not isprime(p) then return false fi;

%F x:= 0;

%F do

%F x:= numtheory:-primroot(x,p);

%F if x = FAIL then return false fi;

%F if x &^ (p-1) mod p^2 = 1 then return true fi;

%F od

%F end proc:

%F select(filter, [2, seq(i,i=3..2000,2)]); # _Robert Israel_, Dec 01 2016

%e 14 is a primitive root of 29 but not of 29^2.

%o (PARI) forprime(p=2,,for(a=1,p-1,if(znorder(Mod(a,p))==p-1&Mod(a,p^2)^(p-1)==1,print1(p,", ");break()))) \\ _Jeppe Stig Nielsen_, Jul 31 2015

%Y Cf. A055578, A060504, A134307.

%K nonn,changed

%O 1,1

%A _Jud McCranie_, Mar 22 2001

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.