Fibonacci-like sequences

Probability Level 4

Conside The Fibonacci sequence is defined by f1=1,f2=1,fn=fn1+fn2 for n3.f_1 = 1, f_2 = 1, f_n = f_{n-1} + f_{n-2} \text{ for } n \geq 3. We have that f13=233.f_{13} = 233. Consider a sequence such that

g1=1,g2=x,gn=gn1+gn2 for n3.g_1 = 1, g_2 = x, g_n = g_{n-1} + g_{n-2} \text{ for } n \geq 3.

Determine the sum of all positive integer values of x2x \geq 2 for which 233233 is a term of the sequence gg.

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