1.5 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4741000cf542c50ff86 | Problem 263: An engineers' dream come true | 5 | 301912 | problem-263-an-engineers-dream-come-true |
--description--
Consider the number 6. The divisors of 6 are: 1,2,3 and 6.
Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6:
1 = 1
, 2 = 2
, 3 = 1 + 2
, 4 = 1 + 3
, 5 = 2 + 3
, 6 = 6
.
A number n
is called a practical number if every number from 1 up to and including n
can be expressed as a sum of distinct divisors of n
.
A pair of consecutive prime numbers with a difference of six is called a sexy pair (since "sex" is the Latin word for "six"). The first sexy pair is (23, 29).
We may occasionally find a triple-pair, which means three consecutive sexy prime pairs, such that the second member of each pair is the first member of the next pair.
We shall call a number n
such that:
- (
n - 9
,n - 3
), (n - 3
,n + 3
), (n + 3
,n + 9
) form a triple-pair, and - the numbers
n - 8
,n - 4
,n
,n + 4
andn + 8
are all practical,
an engineers’ paradise.
Find the sum of the first four engineers’ paradises.
--hints--
engineersDreamComeTrue()
should return 2039506520
.
assert.strictEqual(engineersDreamComeTrue(), 2039506520);
--seed--
--seed-contents--
function engineersDreamComeTrue() {
return true;
}
engineersDreamComeTrue();
--solutions--
// solution required