Dear all,
I recently wanted to count the number of primes in the sequences 2^n+3
and 2^n-3 (and a few more besides) where n is a positive integer.
After a while I realised that I had no real idea how to do this in racket /
scheme. I think part of my problem is that I really think of the problem in an
imperative way, i.e. "for each n check whether 2^n+3 is prime and if so add one
to a count".
The program at the bottom of my email is what I came up with. I hope it is
clear. I think a more idiomatic racket approach would be to use the for
looping construct but I couldn't quite figure out how to make this do what I
wanted.
I can imagine improving the below by modifying the count-primes-in-seq
procedure to take several "formulas" so I can deal with several sequences at
once. However, the code below is quite slow even just for one sequence so I
imagine that a different approach entirely is what is needed.
So, my question is this: how would you more experienced racketeers write code
for something like this?
I quickly threw together a naive program in Python (a language I'm not too
familiar with either) and it was faster to write and runs quicker. However, to
be quite honest, I am fonder of racket and would rather just get better at
writing racket code for the little things I need to do.
Any guidance is appreciated.
#lang racket
(require math/number-theory)
(define (count-primes-in-seq formula bound)
(let loop ([n 0]
[c 0])
(let ([k (formula n)])
(cond
[(> n bound)
c]
[(and (positive? k) (prime? k))
(loop [+ n 1] [+ c 1])]
[else
(loop [+ n 1] c)]))))
(define bound 1000)
; Primes of the form 2^n-3
(count-primes-in-seq
(λ (n) (- (expt 2 n) 3))
bound)
; Primes of the form 2^n+3
(count-primes-in-seq
(λ (n) (+ (expt 2 n) 3))
bound)
Regards,
Bob Heffernan
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