RE: a(n+1) = log(1+a(n))

[Jacques Gélinas <jacquesg00@hotmail.com>]

Generating plots would involve recalculating the same logarithms
over and over again, which should be avoided by precomputing them.

P1 = precision(1.0);
v = 2; Vh = vector(20000, n, v = log(precision(1+v,P1)));
h(n) = n*(n*Vh[n] - 2) / ( log(n) + (n==1) )

pv(M,N,fn)  = vector(N-M+1,n,fn(M+n-1));
pl(M=1,N=100,fn) = plothraw(pv(M,N,n->n),pv(M,N,fn),1);

pl(1,20000,h)

Jacques Gélinas

P.S. memoize.gp by Kevin Ryde is a more elegant solution.