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 A183919 Characteristic sequence for sin(2Pi/n) being rational. 3
 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 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 Cf. sequence for cos(2Pi/n) is A183918. Sequence in context: A039963 A267537 A329670 * A355449 A058840 A266155 Adjacent sequences: A183916 A183917 A183918 * A183920 A183921 A183922 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jan 13 2011 STATUS approved

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Last modified November 29 09:23 EST 2022. Contains 358422 sequences. (Running on oeis4.)