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A125878 Duplicate of A066674. 15


%S 3,7,11,29,23,53,103,191,47,59,311,149,83,173,283,107,709,367,269,569,

%T 293,317,167,179,389,607,619,643,1091,227,509,263,823,557,1193,907,

%U 1571,653,2339,347,359,1087,383,773,3547,797,2111,2677,5449,2749,467

%N Duplicate of A066674.

%C 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.

%C Comments from _N. J. A. Sloane_, Jan 07 2013 (Start)

%C 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.

%C It also seems likely that this is the same as A035095, but this is an open problem.

%C Conjecture: this sequence contains only primes (this would follow if this is indeed the same as A035095).

%C (End)

%D See A181877.

%Y Cf. A066674, A035095, A125866-A125877.

%K dead

%O 1,1

%A _Artur Jasinski_, Dec 13 2006

%E Edited by _Don Reble_, Apr 24 2007

%E Minor edits by _Ray Chandler_, Oct 20 2011

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Last modified April 18 18:20 EDT 2021. Contains 343089 sequences. (Running on oeis4.)