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 A110258 Denominators in the coefficients that form the odd-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x. 8
 1, 4, 64, 256, 16384, 65536, 1048576, 4194304, 1073741824, 4294967296, 68719476736, 274877906944, 17592186044416, 70368744177664, 1125899906842624, 4503599627370496, 4611686018427387904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Limit A110257(n)/a(n) = limit A110255(2*n-1)/A110256(2*n-1) = 4/Pi. Apart from offset, identical to A056982. LINKS Paul D. Hanna, Table of n, a(n) for n = 1..200 FORMULA a(n) = 4^A005187(n-1). a(n) = A110256(2*n-1). EXAMPLE arctan(1/x) = 1/x - 1/(3*x^3) + 1/(5*x^5) - 1/(7*x^7) +-... = [0; x, 3*x, 5/4*x, 28/9*x, 81/64*x, 704/225*x, 325/256*x, 768/245*x, 20825/16384*x, 311296/99225*x, 83349/65536*x, 1507328/480249*x, 1334025/1048576*x, 3145728/1002001*x,...] = 1/(x + 1/(3*x + 1/(5/4*x + 1/(28/9*x + 1/(81/64*x +...))))). The coefficients of x in the even-indexed partial quotients converge to Pi: {3, 28/9, 704/225, 768/245, 311296/99225, ...}. The coefficients of x in the odd-indexed partial quotients converge to 4/Pi: {1, 5/4, 81/64, 325/256, 20825/16384, ...}. PROG (PARI) {a(n)=denominator(subst((contfrac( sum(k=0, 2*n+1, (-1)^k/x^(2*k+1)/(2*k+1)), 2*n+2))[2*n], x, 1))} (PARI) a(n)=4^(2*n-vecsum(binary(n-1))-2) \\ Charles R Greathouse IV, Apr 09 2012 CROSSREFS See A056982 for another version of this sequence. Cf. A110257 (numerators), A110255/A110256 (continued fraction), A110259/A110260. Sequence in context: A260182 A056229 A062271 * A056982 A030994 A299147 Adjacent sequences:  A110255 A110256 A110257 * A110259 A110260 A110261 KEYWORD frac,nonn,easy AUTHOR Paul D. Hanna, Jul 18 2005 EXTENSIONS Edited by N. J. A. Sloane, Jun 05 2007 STATUS approved

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)