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A350121
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Increasing sequence of primes p == 3 (mod 4) such that all of 2,3,5,...,prime(n) are primitive roots mod p.
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1
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3, 19, 907, 1747, 2083, 101467, 350443, 916507, 1014787, 6603283, 27068563, 45287587, 226432243, 243060283, 3946895803, 5571195667, 9259384843, 19633449763, 229012273627
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OFFSET
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1,1
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COMMENTS
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It is possible, although rather unlikely, that any primes congruent to 3 (mod 4) will appear in A213052.
a(19) > 10^11.
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LINKS
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EXAMPLE
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a(2) = 19 since 19 is the smallest prime (congruent to 3 (mod 4)) such that the first two primes (2 and 3) are primitive roots.
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MATHEMATICA
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max=0; Do[n=Prime@i; If[Mod[n, 4]==3, k=1; While[MultiplicativeOrder[Prime@k, n]==n-1, k++]; If[k-1>max, Print@n; max++]], {i, 10^6}] (* Giorgos Kalogeropoulos, Dec 17 2021 *)
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PROG
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(PARI)
N=10^10;
default(primelimit, N);
A=2;
{ forprime (p=3, N,
if (p%4==3,
q = 1;
forprime (a=2, A,
if ( znorder(Mod(a, p)) != p-1, q=0; break() );
);
if ( q, A=nextprime(A+1); print1(p, ", ") );
);
); }
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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