A006243 Extracting a square root. (Formerly M5412)

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

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

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

Adjacent sequences: A006240 A006241 A006242 * A006244 A006245 A006246

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Offset changed by Sean A. Irvine, Feb 08 2017

Status

approved