Problem 52669. Count the primes in Collatz sequences

Created by ChrisR

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Several Cody problems (21, 69, 42937, 44448, 44784, 52422) involve Collatz sequences. These start with a seed n. If n is odd, the next element is , and if n is even, the next element is . For example, if the seed is 3, then the sequence is 3, 10, 5, 16, 8, 4, 2, 1. The Collatz conjecture is that all of these sequences terminate at the value 1; that is, all seeds lead to terminating sequences. 
This problem deals with the number of primes in the sequence. With a seed of 3, the number of primes is 3 (2, 3, 5). 
Write a function to determine the numbers of primes in the sequences with seeds of 1 to the input number. See the test suite for banned terms and commands. 

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Last Solution submitted on Dec 21, 2025

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Tim on 8 Sep 2021

I notice that p=isprime(x) can be a lot slower than p=ismember(x,primes(max(x))); for x=1:1e7, the former takes about 100 seconds and the latter takes about 0.1 seconds.

ChrisR on 11 Sep 2021

Nice observation. I'll keep that one in mind.

Nicolas Douillet on 10 Jul 2025

Actually for the first case (seed n = 1), the answer should be 1 and not 0, since the corresponding Collatz sequence is the loop (1, 4, 2), should'nt it be ?

Nicolas Douillet on 10 Jul 2025

Ok I suppose we don't count the special case of this infinite loop since we do have to stop the sequence at a point ! (1)

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Problem 52669. Count the primes in Collatz sequences

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Problem 52669. Count the primes in Collatz sequences

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