The Hailstone sequence of numbers can be generated from a starting positive integer, n by:
If n is 1 then the sequence ends. If n is even then the next n of the sequence = n/2
If n is odd then the next n of the sequence = (3 * n) + 1
The (unproven) Collatz conjecture is that the hailstone sequence for any starting number always terminates.
The hailstone sequence is also known as hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as the Collatz sequence.
Task: Create a routine to generate the hailstone sequence for a number. Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with27, 82, 41, 124
and ending with 8, 4, 2, 1
Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length. (But don't show the actual sequence!)See also:
xkcd (humourous).
hailstoneSequence
is a function.
testString: assert(typeof hailstoneSequence === 'function', 'hailstoneSequence
is a function.');
- text: hailstoneSequence()
should return [[27,82,41,124,8,4,2,1], [351, 77031]]
testString: assert.deepEqual(hailstoneSequence(), res, 'hailstoneSequence()
should return [[27,82,41,124,8,4,2,1], [351, 77031]]
');
```