The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.
How many n-digit positive integers exist which are also an nth power?
let naturalNumbers = Seq.unfold (fun state -> Some(state, state+1)) 1 // define function to find the number of n digit numbers which are also nth power let f n = naturalNumbers |> Seq.map (fun n' -> pown (bigint(n')) n) |> Seq.skipWhile (fun n' -> n'.ToString().Length < n) |> Seq.takeWhile (fun n' -> n'.ToString().Length = n) |> Seq.length let answer = naturalNumbers |> Seq.map f |> Seq.takeWhile (fun l -> l > 0) |> Seq.sum
I’m an AWS Serverless Hero and the author of Production-Ready Serverless. I have run production workload at scale in AWS for nearly 10 years and I have been an architect or principal engineer with a variety of industries ranging from banking, e-commerce, sports streaming to mobile gaming. I currently work as an independent consultant focused on AWS and serverless.
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.
- Lambda optimization tip – enable HTTP keep-alive
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- Many faced threats to Serverless security
- We can do better than percentile latencies
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- Yubl’s road to Serverless
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- AWS Lambda – compare coldstart time with different languages, memory and code sizes
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