A282180 a(n+1) = a(n)*(a(n)^2 - 3) with a(0) = 8.
8, 488, 116212808, 1569502402942700328379688, 3866214585126515728777536857817155683642224883875510905654220958052649608
Offset: 0
Keywords
Links
- E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646.
Crossrefs
Programs
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Magma
[n eq 1 select 8 else Self(n-1)^3 - 3*Self(n-1): n in [1..6]];
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Mathematica
RecurrenceTable[{a[0] == 8, a[n] == a[n-1]^3 - 3 a[n-1]}, a, {n, 8}]
Formula
a(n) = (4 + sqrt(15))^(3^n) + (4 - sqrt(15))^(3^n). - Bruno Berselli, Feb 10 2017
a(n) = -2*cos(3^n * arccos(-4)). - Daniel Suteu, Feb 10 2017