A113401 -id:A113401 - cp's OEIS frontend

A113402 Algebraic degree of cos(Pi/n) for constructible n-gons (A003401).

1, 1, 1, 2, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 512, 512, 512, 512, 512, 512, 512, 512, 512

Offset: 1

Eric W. Weisstein, Oct 28 2005

a(n) is always a power of 2.
It would appear that a(n) <= a(n+1) and that for a(n)=2^k, the count for k beginning with 0 is 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, ...; or that the count for k is k+2 for k > 0. - Robert G. Wilson v, Jul 31 2014
Apparently v_2(a(n)) = A052146(n-1) for n >= 2 where v_2 is the 2-adic valuation. - Joerg Arndt, Jul 29 2014 [incorrect for n >= 561, Joerg Arndt, Mar 03 2019]

Robert G. Wilson v, Table of n, a(n) for n = 1..1632
Eric Weisstein's World of Mathematics, Trigonometry Angles

Cf. A000217, A002024, A003401, A055034, A113401.

f[n_] := Exponent[MinimalPolynomial[Cos[Pi/n]][x], x]; Table[ f@ n, {n, Select[ Range@ 1300, IntegerQ[ Log[2, EulerPhi[#]]] &]}] (* Robert G. Wilson v, Jul 28 2014 *)
A092506 = {2, 3, 5, 17, 257, 65537}; s = Sort[Times @@@ Subsets@ A092506]; mx = 2500; t = Union@ Flatten@ Table[(2^n)*s[[i]], {i, 64}, {n, 0, Log2[mx/s[[i]]]}]; f[n_] := EulerPhi[ 2n]/2; f[1] = 1; f@# & /@ t (* Robert G. Wilson v, Jul 28 2014 *)

cp's OEIS Frontend

A113402 Algebraic degree of cos(Pi/n) for constructible n-gons (A003401).

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