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URL: https://oeis.org/A006243

⇱ A006243 - OEIS

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A006243
Extracting a square root.
4
198, 7761798, 467613464999866416198, 102249460387306384473056172738577521087843948916391508591105798
OFFSET
1,1
REFERENCES
Jeffrey Shallit, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646.
FORMULA
a(1) = 198, a(n) = a(n-1)^3 - 3*a(n-1). - Sean A. Irvine, Feb 08 2017
a(n) = (99 + 70*sqrt(2))^(3^(n-1)) + (99 - 70*sqrt(2))^(3^(n-1)). - Bruno Berselli, Feb 10 2017
MATHEMATICA
RecurrenceTable[{a[1]==198, a[n]==a[n-1]^3 - 3 a[n-1]}, a, {n, 8}] (* Vincenzo Librandi, Feb 09 2017 *)
PROG
(Magma) [n eq 1 select 198 else Self(n-1)^3-3*Self(n-1): n in [1..5]]; // Vincenzo Librandi, Feb 09 2017
CROSSREFS
Cf. A006242, A112845 (differs only for the initial 6).
Sequence in context: A270849 A324454 A097731 * A171391 A151738 A128312
KEYWORD
nonn
EXTENSIONS
Offset changed by Sean A. Irvine, Feb 08 2017
STATUS
approved