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A006242 Extracting a square root.
(Formerly M4758)
3
10, 970, 912670090, 760223786832147978143718730, 439363892017598816969702791108195858981800447259539613873486126455827777484460810 (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..7

FORMULA

a(1) = 10, a(n) = a(n-1)^3 - 3*a(n-1) [From Escott]. - Sean A. Irvine, Feb 08 2017

a(n) = (5 + 2*sqrt(6))^(3^(n-1)) + (5 - 2*sqrt(6))^(3^(n-1)). - Bruno Berselli, Feb 10 2017

MATHEMATICA

RecurrenceTable[{a[1]==10, a[n]==a[n-1]^3 - 3 a[n-1]}, a, {n, 8}] (* Vincenzo Librandi, Feb 09 2017 *)

PROG

(MAGMA) [n eq 1 select 10 else Self(n-1)^3-3*Self(n-1): n in [1..5]]; // Vincenzo Librandi, Feb 09 2017

CROSSREFS

Cf. A006243.

Sequence in context: A015008 A194791 A159869 * A163566 A168520 A200993

Adjacent sequences:  A006239 A006240 A006241 * A006243 A006244 A006245

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane.

EXTENSIONS

New offset and a(5) from Sean A. Irvine, Feb 08 2017

STATUS

approved

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Last modified February 24 02:57 EST 2017. Contains 282560 sequences.