A282181 a(n+1) = a(n)*(a(n)^2 - 3) with a(0) = 9.

9, 702, 345946302, 41402453463588423862656702, 70970560162990674076135964501350282214065161983319841388247466125133356250302

Offset: 0

Author

Vincenzo Librandi, Feb 10 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. similar sequences listed in A282180.

Programs

Magma

[n eq 1 select 9 else Self(n-1)^3-3*Self(n-1): n in [1..6]];

Mathematica

RecurrenceTable[{a[0] == 9, a[n] == a[n-1]^3 - 3 a[n-1]}, a, {n, 8}]

Formula

a(n) = ((9 + sqrt(77))/2)^(3^n) + ((9 - sqrt(77))/2)^(3^n). - Bruno Berselli, Feb 10 2017