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 A163262 Denominators of fractions in the approximation of the square root of 2 by means of: f(n) = 3*f(n-1)/(f(n-1)^2+1); with f(1)= 1 1
 1, 2, 13, 493, 735853, 1619459312173, 7875984855578888541679213, 186030029004437379749629399827828117533654561726893 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For root of c: f(n) = (1+c)*f(n-1)/(f(n-1)^2+1). a(9) has 102 digits. - Emeric Deutsch, Jul 29 2009 LINKS MAPLE f[1] := 1: for n from 2 to 10 do f[n] := 3*f[n-1]/(1+f[n-1]^2) end do: seq(denom(f[n]), n = 1 .. 8); # Emeric Deutsch, Jul 29 2009 PROG (PARI) f(n) = if (n==1, 1, 3*f(n-1)/(f(n-1)^2+1)); a(n) = denominator(f(n)); \\ Michel Marcus, Mar 04 2019 CROSSREFS Cf. A002193 (sqrt(2)), A163261 (numerators). Cf. A001601 and A051009: Newton's method. Sequence in context: A082751 A120935 A015183 * A132570 A013048 A012981 Adjacent sequences:  A163259 A163260 A163261 * A163263 A163264 A163265 KEYWORD nonn,frac AUTHOR Mark Dols, Jul 23 2009 EXTENSIONS a(7) and a(8) from Emeric Deutsch, Jul 29 2009 Name edited by Michel Marcus, Mar 04 2019 STATUS approved

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Last modified March 20 05:17 EDT 2019. Contains 321344 sequences. (Running on oeis4.)