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 A112845 Recurrence a[k]==a[k-1]^3-3a[k-1] with a[0]=6. 4
 6, 198, 7761798, 467613464999866416198, 102249460387306384473056172738577521087843948916391508591105798 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Identical to A006243 apart from the initial term. For some general remarks on this recurrence see A001999. - Peter Bala, Nov 13 2012 REFERENCES E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646. N. J. Fine, Infinite products for k-th roots. Amer. Math. Monthly, Vol. 84, No. 8, Oct. 1977 LINKS Eric Weisstein's World of Mathematics, Pierce Expansion FORMULA -2*Cos[3^k*ArcCos[ -3]] From Peter Bala, Nov 13 2012: (Start) a(n) = (3 + 2*sqrt(2))^(3^n) + (3 - 2*sqrt(2))^(3^n). Product {n = 0..inf} (1 + 2/(a(n) - 1)) = sqrt(2). (End) CROSSREFS Cf. A006275, A006276. Cf. A006243. [From R. J. Mathar, Aug 15 2008]. A001999, A219160, A219161. Sequence in context: A156122 A086065 A200824 * A109058 A003743 A115491 Adjacent sequences:  A112842 A112843 A112844 * A112846 A112847 A112848 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Sep 21, 2005 STATUS approved

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