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A006243 Extracting a square root.
(Formerly M5412)
4
198, 7761798, 467613464999866416198, 102249460387306384473056172738577521087843948916391508591105798 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646.

Jeffrey Shallit, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..6

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: A278017 A270849 A097731 * A171391 A151738 A128312

Adjacent sequences:  A006240 A006241 A006242 * A006244 A006245 A006246

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Offset changed by Sean A. Irvine, Feb 08 2017

STATUS

approved

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Last modified February 21 11:53 EST 2017. Contains 282443 sequences.