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A065428
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Numbers n such that all x^2 mod n are nonprimes.
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3
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1, 2, 3, 4, 5, 8, 12, 15, 16, 24, 28, 40, 48, 56, 60, 72, 88, 112, 120, 168, 232, 240, 280, 312, 408, 520, 760, 840, 1320, 1848
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All numbers in this sequence except 56 are idoneal (A000926) - Joerg Arndt, Jul 13 2005
No more terms < 10^6. - T. D. Noe, Aug 10 2007
No more terms < 10^11. [From Charles R Greathouse IV, Dec 15 2008]
Numbers x such that all x^3 mod n are nonprimes are 1, 2, 7, 9, 63, and apparently no more.
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LINKS
| Joerg Arndt, Fxtbook, p. 784
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MATHEMATICA
| t={}; Do[s=Union[Mod[Range[n]^2, n]]; If[Select[s, PrimeQ]=={}, AppendTo[t, n]], {n, 1000}]; t (* T. D. Noe, Aug 10 2007 *)
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PROG
| (PARI) for(n=1, 10^9, q=1; for(x=1, n-1, if(isprime(x*x%n), q=0; break())); if(q, print1(n, ", ")));
(Haskell)
a065428 n = a065428_list !! (n-1)
a065428_list = filter f [1..] where
f n = all (== 0) $ map (a010051 . (`mod` n) . (^ 2)) [1..n-1]
-- Reinhard Zumkeller
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CROSSREFS
| Cf. A179402 (x^4 mod n).
Cf. A010051, A000196, A000290.
Sequence in context: A122700 A048486 A179402 * A059747 A094087 A017821
Adjacent sequences: A065425 A065426 A065427 * A065429 A065430 A065431
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KEYWORD
| nonn,nice,more
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AUTHOR
| Joerg Arndt (arndt(AT)jjj.de), Nov 16 2001
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