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Diffstat (limited to 'julia/014-longest_collatz_sequence.jl')
| -rw-r--r-- | julia/014-longest_collatz_sequence.jl | 24 |
1 files changed, 24 insertions, 0 deletions
diff --git a/julia/014-longest_collatz_sequence.jl b/julia/014-longest_collatz_sequence.jl new file mode 100644 index 0000000..1edaf98 --- /dev/null +++ b/julia/014-longest_collatz_sequence.jl @@ -0,0 +1,24 @@ +### +# Longest Collatz sequence +# Problem 14 +# +# The following iterative sequence is defined for the set of positive integers: +# n → n/2 (n is even)n → 3n + 1 (n is odd) +# Using the rule above and starting with 13, we generate the following sequence: +# 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 +# It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. +# Although it has not been proved yet (Collatz Problem), it is thought that all starting +# numbers finish at 1. +# Which starting number, under one million, produces the longest chain? +# NOTE: Once the chain starts the terms are allowed to go above one million. +### + +function collatz_length(n) + n == 1 && return 1 + n % 2 == 0 && return 1 + collatz_length(n ÷ 2) + return 1 + collatz_length(3n + 1) +end + +result = argmax([collatz_length(x) for x in 1:(1_000_000 - 1)]) + +println(result) |