A006242 Extracting a square root. (Formerly M4758)

10, 970, 912670090, 760223786832147978143718730, 439363892017598816969702791108195858981800447259539613873486126455827777484460810

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

Vincenzo Librandi, Table of n, a(n) for n = 1..7

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

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

a(n) = 2*T(3^(n-1),5), where T(n,x) deotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Mar 29 2022

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: A194791 A292669 A159869 * A163566 A168520 A200993

Adjacent sequences: A006239 A006240 A006241 * A006243 A006244 A006245

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved