Erdős problem 267 · problems.science

If $n_1 < n_2 < \cdots$ with $n_{k+1}/n_k \ge c > 1$ , must $\sum_k 1/F_{n_k}$ be irrational? The proposed proof closes the range $1 < c < 2$ left open by earlier criteria.

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FormalConjectures/ErdosProblems/

267.lean

Retained formal statement2 of 4

The sum $\sum_n \frac 1 {F_{n}}$ itself was proved to be irrational by André-Jeannin.

Ref: André-Jeannin, Richard, _Irrationalité de la somme des inverses de certaines suites récurrentes_.

FormalConjectures/ErdosProblems/267.leanErdos267.erdos_267.variants.fibonacci_inverse_sum1 lineExact file

1Irrational (∑' (k : ℕ), 1 / ↑(Nat.fib k))

SolvedStatement only, no proof

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