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The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
What 12-digit number do you form by concatenating the three terms in this sequence?
open System.Collections let rec distribute e = function |  -> [[e]] | x::xs' as xs -> (e::xs)::[for xs in distribute e xs' -> x::xs] let rec permute = function |  -> [] | e::xs -> List.collect (distribute e) (permute xs) let rec comb n l = match n, l with | 0, _ -> [] | _,  ->  | k, (x::xs) -> List.map ((@) [x]) (comb (k-1) xs) @ comb k xs let max = 9999 // define a cache for holding records of which number is a prime let cache = new BitArray(max+1, true) // using prime sieve to fill out the cache [2..max] |> List.iter (fun n -> if cache.[n] then [2..max] |> Seq.takeWhile (fun m -> n * m <= max) |> Seq.iter (fun m -> cache.[n * m] List.filter (fun n -> cache.[n]) // define function to get the 4-digit prime permutations of a number let getPrimePermutations n = let digitsStr = n.ToString().ToCharArray() |> Array.map string Array.toList digitsStr |> permute |> Seq.distinct |> Seq.map (fun chars -> int(chars |> List.reduce (+))) |> Seq.filter (fun x -> x >= 1000 && cache.[x]) |> Seq.sort |> Seq.toList let answer = primeNumbers |> List.map getPrimePermutations |> List.filter (fun l -> l |> List.length >= 3) |> Seq.distinct |> Seq.toList |> List.map (fun l -> comb 3 l |> List.filter (fun l' -> l'. - l'. = l'. - l'.)) |> List.filter (fun l -> l |> List.length > 0)
The above solution returns two lists:
val answer : int list list list = [[[1487; 4817; 8147]]; [[2969; 6299; 9629]]]
The first of course, correlates to the example given in the brief, the other, is the base for your answer!
Hi, I’m Yan. I’m an AWS Serverless Hero and I help companies go faster for less by adopting serverless technologies successfully.
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.
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We will start at the basics and give you a firm introduction to Lambda and all the relevant concepts and service features (including the latest announcements in 2020). And then gradually ramping up and cover a wide array of topics such as API security, testing strategies, CI/CD, secret management, and operational best practices for monitoring and troubleshooting.
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Check out my new podcast Real-World Serverless where I talk with engineers who are building amazing things with serverless technologies and discuss the real-world use cases and challenges they face. If you’re interested in what people are actually doing with serverless and what it’s really like to be working with serverless day-to-day, then this is the podcast for you.
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. We will also cover latest features from re:Invent 2019 such as Provisioned Concurrency and Lambda Destinations. Enrol now and start learning!
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Here is a complete list of all my posts on serverless and AWS Lambda. In the meantime, here are a few of my most popular blog posts.
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