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A094928
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Let p = n-th prime == 1 mod 8 (A007519); a(n) = smallest prime q such that p is not a square mod q.
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4
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3, 3, 5, 3, 5, 3, 3, 5, 3, 7, 3, 3, 5, 5, 3, 3, 7, 5, 3, 5, 3, 3, 5, 3, 7, 3, 3, 5, 3, 7, 3, 3, 3, 3, 5, 3, 3, 11, 5, 3, 3, 11, 5, 3, 11, 3, 7, 3, 5, 7, 3, 3, 3, 3, 7, 3, 3, 7, 5, 3, 3, 5, 5, 11, 5, 3, 3, 5, 5, 3, 7, 5, 3, 5, 3, 7, 3, 7, 3, 5, 3, 3, 3, 5, 11, 5, 3, 5, 3, 3, 13, 5, 3, 3, 3, 3, 5, 5, 3, 5, 3, 7
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OFFSET
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1,1
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REFERENCES
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M. Kneser, Quadratische Formen, Springer, 2002; see Hilfssatz 18.3.
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LINKS
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FORMULA
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EXAMPLE
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n=3, p = 73, a(3) = q = 5: Legendre(73,5) = -1.
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MAPLE
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f:= proc(p) local q;
q:= 3:
do
if numtheory:-quadres(p, q) = -1 then return q fi;
q:= nextprime(q);
od;
end proc:
map(f, select(isprime, [seq(p, p=1..10000, 8)])); # Robert Israel, May 06 2019
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MATHEMATICA
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f[n_] := Prime[ Position[ JacobiSymbol[n, Select[Range[3, n - 1], PrimeQ[ # ] &]], -1][[1, 1]] + 1]; f /@ Select[ Prime[ Range[435]], Mod[ #, 8] == 1 &] (* Robert G. Wilson v, Jun 23 2004 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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