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A115586 Prime moduli p for which 2 is neither a quadratic residue nor a primitive root. 5

%I #12 Apr 02 2018 21:03:46

%S 43,109,157,229,251,277,283,307,331,397,499,571,643,683,691,733,739,

%T 811,971,997,1013,1021,1051,1069,1093,1163,1181,1429,1459,1579,1597,

%U 1613,1627,1699,1709,1723,1789,1811,1933,2003,2011,2179,2203,2251

%N Prime moduli p for which 2 is neither a quadratic residue nor a primitive root.

%H Robert Israel, <a href="/A115586/b115586.txt">Table of n, a(n) for n = 1..10000</a>

%p select(p -> isprime(p) and numtheory:-order(2,p) <> p-1, [seq(seq(8*i+j,j=[3,5]),i=1..1000)]); # _Robert Israel_, Apr 02 2018

%t Select[Prime[Range[400]], MultiplicativeOrder[2, #] != # - 1 && JacobiSymbol[2, #] == -1 &] (* _Alonso del Arte_, Jun 08 2014 *)

%o (PARI) is(n)=n>2&&isprime(n)&&kronecker(2,n)!=1&&znprimroot(n)!=2 \\ _Lear Young_, Mar 26 2014

%Y Cf. A001122, A001132, A001133, A003629.

%Y Intersection of A216838 and A003629.

%K nonn

%O 1,1

%A _Don Reble_, Mar 11 2006

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Last modified June 12 16:06 EDT 2024. Contains 373333 sequences. (Running on oeis4.)