Yellowstone sequence: Difference between revisions

=={{header|Nim}}==

===Procedure version===

This version uses a set and, so, is limited to 65536 elements. It is easy to change this limit by using a HashSet (standard module “sets”) instead of a set. See the iterator version which uses such a HashSet.

<lang Nim>import math

proc yellowstone(n: int): seq[int] =

assert n >= 3

result = @[1, 2, 3]

var present = {1, 2, 3}

var start = 4

while result.len < n:

var candidate = start

while true:

if candidate notin present and gcd(candidate, result[^1]) == 1 and gcd(candidate, result[^2]) != 1:

result.add candidate

present.incl candidate

while start in present: inc start

break

inc candidate

echo yellowstone(30)</lang>

{{out}}

<pre>@[1, 2, 3, 4, 9, 8, 15, 14, 5, 6, 25, 12, 35, 16, 7, 10, 21, 20, 27, 22, 39, 11, 13, 33, 26, 45, 28, 51, 32, 17]</pre>

===Iterator version===

This version uses a HashSet, but using a set as in the previous version is possible if we accept the limit of 65536 elements.

<lang Nim>import math, sets

iterator yellowstone(n: int): int =

assert n >= 3

for i in 1..3: yield i

var present = [1, 2, 3].toHashSet

var prevLast = 2

var last = 3

var start = 4

for _ in 4..n:

var candidate = start

while true:

if candidate notin present and gcd(candidate, last) == 1 and gcd(candidate, prevLast) != 1:

yield candidate

present.incl candidate

prevLast = last

last = candidate

while start in present: inc start

break

inc candidate

for n in yellowstone(30):

stdout.write " ", n

echo()</lang>

{{out}}

<pre> 1 2 3 4 9 8 15 14 5 6 25 12 35 16 7 10 21 20 27 22 39 11 13 33 26 45 28 51 32 17</pre>