Here we reused the technique from Problem 44 for quickly asserting that a number is in the range of a function by verifying that n = f (f-1(n)). We could also have tested that f-1(n) is integral.

let problem45a = let pent n = n*(3L*n-1L)/2L let pentInv n = (1L + sqrtL(24L*n + 1L))/6L let isPent n = (n = (pent (pentInv n))) let hex n = n*(2L*n-1L) let hexInv n = (1L + sqrtL(8L*n + 1L))/4L let isHex n = (n = (hex (hexInv n))) let tri n = n*(n+1L)/2L let rec triSeq n = seq {yield tri n; yield! triSeq (n+1L)} triSeq 286L |> Seq.find (fun n -> isPent n && isHex n)

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