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A088817
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Numbers k such that Cyclotomic(2k,k) is prime.
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3
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1, 2, 3, 4, 5, 9, 17, 36, 157, 245, 352, 3977
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OFFSET
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1,2
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COMMENTS
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This is a generalization of A056826. Note that (n^n+1)/(n+1) = cyclotomic(2n,n) when n is prime. These are probable primes for n > 352. No others < 4700.
All terms of this sequence that are greater than 3 are congruent to 0 or 1 mod 4. In general, if k = s^2*t where t is squarefree and t == 2, 3 (mod 4), then Cyclotomic(2k,t*x^2) is the product of two polynomials. See the Wikipedia link below. - Jianing Song, Sep 25 2019
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LINKS
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MATHEMATICA
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Do[p=Prime[n]; If[PrimeQ[Cyclotomic[2n, n]], Print[p]], {n, 100}]
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PROG
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CROSSREFS
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Cf. A056826 ((k^k+1)/(k+1) is prime), A070519 (cyclotomic(k,k) is prime), A088875 (cyclotomic(k,-k) is prime).
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KEYWORD
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hard,nonn
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AUTHOR
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STATUS
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approved
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