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A002224
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Smallest prime p of form p = 8k+1 such that first n primes (p_1=2, ..., p_n) are quadratic residues mod p.
(Formerly M5040 N2176)
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13
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17, 73, 241, 1009, 2689, 8089, 33049, 53881, 87481, 483289, 515761, 1083289, 3818929, 3818929, 9257329, 22000801, 48473881, 48473881, 175244281, 427733329, 427733329, 898716289, 8114538721, 9176747449, 23616331489, 23616331489, 23616331489, 196265095009, 196265095009, 196265095009, 196265095009, 2871842842801, 2871842842801, 2871842842801, 26437680473689
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XV.
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LINKS
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EXAMPLE
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32^2 = 2 mod 73, 21^2 = 3 mod 73.
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MATHEMATICA
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f[n_] := Block[{k = 2}, While[JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]] (* Robert G. Wilson v *)
np[] := While[p = NextPrime[p]; Mod[p, 8] != 1]; p = 2; A002224 = {}; pp = {2}; np[]; While[Length[A002224] < 25, If[Union[JacobiSymbol[#, p] &[pp]] === {1}, AppendTo[pp, NextPrime[Last[pp]]]; Print[p]; AppendTo[A002224, p], np[]]]; A002224 (* Jean-François Alcover, Sep 09 2011 *)
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PROG
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(PARI) a(n, startAt=17)=my(v=primes(n)); forprime(p=startAt, , if(p%8>1, next); for(i=1, n, if(kronecker(v[i], p)<1, next(2))); return(p)) \\ Charles R Greathouse IV, Jun 26 2017
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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