This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112845 #26 Jul 23 2025 14:29:26
%S A112845 6,198,7761798,467613464999866416198,
%T A112845 102249460387306384473056172738577521087843948916391508591105798
%N A112845 Recurrence a(n) = a(n-1)^3 - 3*a(n-1) with a(0) = 6.
%C A112845 Identical to A006243 apart from the initial term. For some general remarks on this recurrence see A001999. - _Peter Bala_, Nov 13 2012
%H A112845 G. C. Greubel, <a href="/A112845/b112845.txt">Table of n, a(n) for n = 0..6</a>
%H A112845 E. B. Escott, <a href="http://www.jstor.org/stable/2301484">Rapid method for extracting a square root</a>, Amer. Math. Monthly, 44 (1937), 644-646.
%H A112845 N. J. Fine, <a href="http://www.jstor.org/stable/2321014">Infinite products for k-th roots</a>, Amer. Math. Monthly Vol. 84, No. 8, Oct. 1977, 629-630.
%H A112845 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>
%F A112845 a(n) = -2*cos(3^n*arccos(-3)).
%F A112845 From _Peter Bala_, Nov 13 2012: (Start)
%F A112845 a(n) = (3 + 2*sqrt(2))^(3^n) + (3 - 2*sqrt(2))^(3^n).
%F A112845 Product {n = 0..inf} (1 + 2/(a(n) - 1)) = sqrt(2).
%F A112845 (End)
%t A112845 RecurrenceTable[{a[n] == a[n - 1]^3 - 3*a[n - 1], a[0] == 6}, a, {n,
%t A112845 0, 5}] (* _G. C. Greubel_, Dec 30 2016 *)
%t A112845 NestList[#^3-3#&,6,5] (* _Harvey P. Dale_, Jul 23 2025 *)
%Y A112845 Cf. A006275, A006276.
%Y A112845 Cf. A006243. - _R. J. Mathar_, Aug 15 2008
%Y A112845 Cf. A001999, A219160, A219161.
%K A112845 nonn,easy
%O A112845 0,1
%A A112845 _Eric W. Weisstein_, Sep 21 2005