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 A332091 Decimal expansion of the arithmetic-geometric mean AGM(1, 1, 2) defined as limit of the sequence x(n+1) = P(x(n)) with x(0) = (1, 1, 2) and P(a,b,c) = ((a + b + c)/3, sqrt((ab + ac + bc)/3), (abc)^(1/3)). 1
 1, 2, 9, 4, 5, 7, 5, 1, 0, 8, 1, 1, 6, 6, 1, 2, 6, 4, 3, 4, 4, 8, 6, 4, 3, 4, 9, 8, 2, 1, 0, 0, 3, 5, 3, 6, 7, 4, 0, 3, 7, 9, 7, 2, 7, 2, 1, 5, 6, 4, 2, 4, 5, 8, 6, 8, 0, 8, 6, 6, 4, 1, 7, 2, 3, 9, 5, 6, 5, 9, 8, 7, 4, 8, 5, 8, 9, 6, 2, 0, 5, 9, 7, 5, 6, 5, 9, 8, 7, 6, 7, 6, 7, 1, 4, 2, 5, 6, 4, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See the main entry A332093 for more information on the multi-argument AGM(...) used here. One main motivation for these entries is to find exact formulas for this function which seems not yet well studied in the literature, or at least for particular values like this one, A332092 = AGM(1,2,2) and A332093 = AGM(1,2,3). Any references to possibly existing works using this definition would be welcome. Other 3-argument generalizations of the AGM have been proposed (cf. A332093) which will give different values for AGM(1,1,2). LINKS Table of n, a(n) for n=1..101. Vladimir Reshetnikov, Arithmetic-geometric mean of 3 numbers, math.StackExchange.com, May 22 2016. User Mathlover, To find the limit of three terms mean iteration, math.StackExchange.com, Jul 12 2013. Wikipedia, Arithmetic-geometric mean, created Jan 2, 2002. EXAMPLE 1.294575108116612643448643498210035367403797272156424586808664172... PROG (PARI) f(k, x, S)={forvec(i=vector(k, i, [1, #x]), S+=vecprod(vecextract(x, i)), 2); S/binomial(#x, k)} \\ normalized k-th elementary symmetric polynomial in x AGM(x)={until(x[1]<=x[#x], x=[sqrtn(f(k, x), k)|k<-[1..#x]]); vecsum(x)/#x} default(realprecision, 100); digits(AGM([1, 1, 2])\.1^100) CROSSREFS Cf. A332092 (AGM(1,2,2)), A332093 (AGM(1,2,3)). Cf. other sequences related to the AGM (of two numbers): A061979, A080504, A090852 ff, A127758 ff. Sequence in context: A248682 A222239 A281384 * A203648 A300889 A275807 Adjacent sequences: A332088 A332089 A332090 * A332092 A332093 A332094 KEYWORD nonn,cons AUTHOR M. F. Hasler, Sep 18 2020 STATUS approved

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Last modified June 2 02:47 EDT 2023. Contains 363081 sequences. (Running on oeis4.)