Project Euler – Problem 45 Solution

Check out my new course Learn you some Lambda best practice for great good! and learn the best practices for performance, cost, security, resilience, observability and scalability.


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 |> T
let PSeq = naturalNumbers 165I |> P
let HSeq = naturalNumbers 143I |> H

let answer =
    |> 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
Liked this article? Support me on Patreon and get direct help from me via a private Slack channel or 1-2-1 mentoring.
Subscribe to my newsletter

Hi, I’m Yan. I’m an AWS Serverless Hero and the author of Production-Ready Serverless.

I specialise in rapidly transitioning teams to serverless and building production-ready services on AWS.

Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.

Hire me.

Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. Enrol now and enjoy a special preorder price of £9.99 (~$13).

Start Learning

Are you working with Serverless and looking for expert training to level-up your skills? Or are you looking for a solid foundation to start from? Look no further, register for my Production-Ready Serverless workshop to learn how to build production-grade Serverless applications!

Find a workshop near you