

A125878


a(n) = the least number k such that cos(2pi/k) is an algebraic number of a prime(n)smooth degree, but not prime(n1)smooth.


16



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

1,1


COMMENTS

Comments from N. J. A. Sloane, Jan 07 2013 (Start)
This is a duplicate of A066674. This follows from the following argument. The degree of the minimal polynomial of cos(2pi/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(n1) 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).
(End)


REFERENCES

See A181877.


LINKS

Table of n, a(n) for n=1..51.


CROSSREFS

Cf. A066674, A035095, A125866A125877.
Sequence in context: A211674 A035095 A066674 * A126112 A194373 A156210
Adjacent sequences: A125875 A125876 A125877 * A125879 A125880 A125881


KEYWORD

nonn


AUTHOR

Artur Jasinski, Dec 13 2006


EXTENSIONS

Edited by Don Reble, Apr 24 2007
Minor edits by Ray Chandler, Oct 20 2011


STATUS

approved



