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3, 7, 11, 29, 23, 53, 103, 191, 47, 59, 311, 149, 83, 173, 283, 107, 709, 367, 269, 569, 293, 317, 167, 179, 389, 607, 619, 643, 1091, 227, 509, 263, 823, 557, 1193, 907, 1571, 653, 2339, 347, 359, 1087, 383, 773, 3547, 797, 2111, 2677, 5449, 2749, 467
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OFFSET
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1,1
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COMMENTS
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Original name was: a(n) = the least number k such that cos(2pi/k) is an algebraic number of a prime(n)-smooth degree, but not prime(n-1)-smooth.
This is a duplicate of A066674. This follows from the following argument. The degree of the minimal polynomial of cos(2*Pi/k) is phi(k)/2, where phi is Euler's totient function. Then a(n) is the least number k such that prime(n) is the largest prime dividing phi(k) and prime(n-1) does not divide phi(k)/2. For the rest of the proof see Bjorn Poonen's remarks in A066674.
It also seems likely that this is the same as A035095, but this is an open problem.
Conjecture: this sequence contains only primes (this would follow if this is indeed the same as A035095).
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KEYWORD
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dead
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STATUS
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approved
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