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 A140666 A triangle of coefficients of the difference of prime cyclotomic doubled polynomials: p(x,n)=(c(x,Prime[n])-c(x,2*Prime[n]))/x. 0
 1, -1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums are: {0, 2, 4, 6, 10, 12, 16, 18, 22, 28, ...} The factor x is used instead of 2x to get an integer n=1 term. p(x,n)/2 are related to the double product:two primes n,m such that Cyclotomic[Prime[n], x]* Cyclotomic[2*Prime[n]=(Cyclotomic[Prime[m], x] - Cyclotomic[2*Prime[m], x])/(2*x) LINKS FORMULA c(x,n)=CyclotomicPolynomial; c(x,Prime[n])=(x^Prime[n]-1)/(x-1); p(x,n)=(c(x,Prime[n])-c(x,2*Prime[n]))/x; a(n,m)=Coefficiencts(p(x,n)) EXAMPLE {1, -1}, {2}, {2, 0, 2}, {2, 0, 2, 0, 2}, {2, 0, 2, 0, 2, 0, 2, 0, 2}, {2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2}, {2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2}, {2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2}, {2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2}, {2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2} MATHEMATICA Clear[p, x, n] p[x_, n_] = (Cyclotomic[Prime[n], x] - Cyclotomic[2*Prime[n], x])/x; Table[ExpandAll[p[x, n]], {n, 1, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[a] CROSSREFS Sequence in context: A258040 A215879 A114700 * A202145 A130772 A257076 Adjacent sequences:  A140663 A140664 A140665 * A140667 A140668 A140669 KEYWORD tabf,uned,sign AUTHOR Roger L. Bagula and Gary W. Adamson, Jul 11 2008 STATUS approved

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