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%I M5412 #31 Sep 08 2022 08:44:34
%S 198,7761798,467613464999866416198,
%T 102249460387306384473056172738577521087843948916391508591105798
%N Extracting a square root.
%D Jeffrey Shallit, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A006243/b006243.txt">Table of n, a(n) for n = 1..6</a>
%H 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.
%F a(1) = 198, a(n) = a(n-1)^3 - 3*a(n-1). - _Sean A. Irvine_, Feb 08 2017
%F a(n) = (99 + 70*sqrt(2))^(3^(n-1)) + (99 - 70*sqrt(2))^(3^(n-1)). - _Bruno Berselli_, Feb 10 2017
%t RecurrenceTable[{a[1]==198, a[n]==a[n-1]^3 - 3 a[n-1]}, a, {n, 8}] (* _Vincenzo Librandi_, Feb 09 2017 *)
%o (Magma) [n eq 1 select 198 else Self(n-1)^3-3*Self(n-1): n in [1..5]]; // _Vincenzo Librandi_, Feb 09 2017
%Y Cf. A006242, A112845 (differs only for the initial 6).
%K nonn
%O 1,1
%A _N. J. A. Sloane_.
%E Offset changed by _Sean A. Irvine_, Feb 08 2017
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