OFFSET
1
COMMENTS
The sequence is 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, followed by zeros.
In the I. Niven reference a formula for the algebraic degree of 2*sin(2*Pi/n) is found in theorem 3.9. This theorem is attributed to D. H. Lehmer, but the sine part in the Lehmer reference is wrong (to wit: n=12 has rational value 2*sin(2*Pi/12)=2*sin(Pi/6)= 1. Hence the degree is 1 = phi(12)/4, as in Niven's book, but not phi(12)/2 = 2 as in Lehmer's paper (the Sines-table there is wrong).
REFERENCES
I. Niven, Irrational Numbers, The Math. Assoc. of America, second printing, 1963, distributed by John Wiley and Sons.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
D. H. Lehmer, A Note on Trigonometric Algebraic Numbers, Am. Math. Monthly 40 (3) (1933) 165-6.
FORMULA
a(n) = 1 if sin(2*Pi/n) is rational, and a(n) = 0 if it is irrational.
EXAMPLE
The rational values of 2*sin(2*Pi/n) are 0, 0, 2 and 1 for n=1, 2, 4 and 12, respectively. Otherwise irrational values appear.
PROG
(PARI) A183919(n) = if(n<1, 0, polcoeff( x^1+x^2+x^4+x^12, n)); \\ Antti Karttunen, Dec 24 2018, after code in A089011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 13 2011
STATUS
approved