A248041 Numerators of approximation to 2^(1/3) by Newton's method after n iterations.

1, 4, 91, 1126819, 2146097524939083451

Offset: 0

Author

Kival Ngaokrajang, Jan 11 2015

Keywords

• nonn
• frac

Comments

Denominators are given in A248042.

Examples

			Approximations to 2^(1/3):
n = 1:            4/3 = 1.33333...; error = 0.07341...
n = 2:          91/72 = 1.26388...; error = 0.00396...
n = 3: 1126819/894348 = 1.25993...; error = 0.00001...
...
		

Links

• Eric Weisstein's World of Mathematics, Cube Root
• Wikipedia, Cube Root

Crossrefs

Cf. A002580, A248042.

Formula

a(n) = x(n)/gcd(x(n),y(n))

where x(n) = 2*(a(n-1)^3*A248042(n-1)^2 + A248042(n-1)^5)

and y(n) = 3*a(n-1)^2*A248042(n-1)^3;

x(0) = y(0) = 1.