Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
It can be verified that T285 = P165 = H143 = 40755.
Find the next triangle number that is also pentagonal and hexagonal.
let naturalNumbers n = Seq.unfold (fun state -> Some(state, state + 1I)) n // define the function T, P and H let T n = n * (n + 1I) / 2I let P n = n * (3I * n - 1I) / 2I let H n = n * (2I * n - 1I) // define the sequences for each function from the point the brief left off at let TSeq = naturalNumbers 285I |> Seq.map T let PSeq = naturalNumbers 165I |> Seq.map P let HSeq = naturalNumbers 143I |> Seq.map H let answer = HSeq |> Seq.skip 1 |> Seq.filter (fun h -> PSeq |> Seq.takeWhile (fun p -> p <= h) |> Seq.exists (fun p -> p = h)) |> Seq.filter (fun h -> TSeq |> Seq.takeWhile (fun t -> t <= h) |> Seq.exists (fun t -> t = h)) |> Seq.head
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