# ShareMyScreen/ProjectEuler/0014

What is the longest Collatz sequence for a natural number under 1e6?

Members of a sequence as derived as follows: if the number is odd, multiply it by 3 and add 1; if odd, halve it.

```   (i.>. /)((\$: @ ((-: ` ([:>:3*]) @. (2&|) @ {.) , >:@{:)) ` {: @. (1&=@{.)"1)M.(i.1e6),.1

(i.1e6-1),.1 NB. 1 through 999999 in a column, next to a column of 1s; the latter will be our state, that is, the length of the sequence so far
] M. NB. highly recursive verbs' performance may benefit from memoization
NB.  recurse with the result
NB.  │    else, add one to the legth to the tail and perform the arithmatic on the head, and combine them
NB.  │    │                                                  give the tail, that is, the recorded length of the sequence
NB.  │    │                                                  │     if the sequence has ended (assuming it always does at 1)
NB.  │    │                                                  │     │          for each row
NB.  │_   │_____________________________________________     │_    │_______ _ │_
((\$: @ ((-: ` ([: >: 3 * ]) @. (2&|) @ {.) , >: @ {:) ) ` {: @. (1&= @ {.) "1)
(i. >./) NB. gives the index of greatest number
```