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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(n-1)-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 (list; graph; refs; listen; history; text; internal format)
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(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).

(End)

REFERENCES

See A181877.

LINKS

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

CROSSREFS

Cf. A066674, A035095, A125866-A125877.

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 (djr(AT)nk.ca), Apr 24 2007

Minor edits by Ray Chandler, Oct 20 2011

STATUS

approved

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Last modified March 29 13:17 EDT 2017. Contains 284270 sequences.