A006243 Extracting a square root.

198, 7761798, 467613464999866416198, 102249460387306384473056172738577521087843948916391508591105798

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A006242, A112845 (differs only for the initial 6).

Programs

Magma

[n eq 1 select 198 else Self(n-1)^3-3*Self(n-1): n in [1..5]]; // Vincenzo Librandi, Feb 09 2017

Mathematica

RecurrenceTable[{a[1]==198, a[n]==a[n-1]^3 - 3 a[n-1]}, a, {n, 8}] (* Vincenzo Librandi, Feb 09 2017 *)

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

Extensions

Offset changed by Sean A. Irvine, Feb 08 2017