The Fano index of an n-dimensional well-formed weighted projective space with canonical singularities is at most (s_n-1)(2s_n-3), where s_n is the n-th Sylvester number.
Conrads,Weighted projective spaces and reflexive polytopes, Manuscripta
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On Fano indices of weighted projective spaces
The Fano index of an n-dimensional well-formed weighted projective space with canonical singularities is at most (s_n-1)(2s_n-3), where s_n is the n-th Sylvester number.