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Presumably in a different number base (base 12, eg) it would be a different number that had this reciprocal property. Would it still be in the fibonacci series
by ckemere 6y ago
Presumably in a different number base (base 12, eg) it would be a different number that had this reciprocal property. Would it still be in the fibonacci series in that base?
- stabbles 6y agoCompute the generating function f(x) = sum_n f_n x^n where f_n satisfies your favorite recursion. Compute f(b^-1) where b is your base. For fibonacci f(x) = x / (1 - x - x^2).
- core-questions 6y agoThis was my thought too. If 1/89 in base 10 works, and 89 in the 10th unique term of the series > 1,1,2,3,5,8,13,21,34,55,89,144,... then does 1/144 work in base 11, and 1/233 in base 12? Assuming we of course translate the base-10 number 144 to the appropriate base-11 number (121) first. I'm too bad at math to do this anymore, maybe someone else can tell us ;)