849 B
849 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4be1000cf542c50ffd0 | Problem 337: Totient Stairstep Sequences | 5 | 301995 | problem-337-totient-stairstep-sequences |
--description--
Let {a1, a2,..., an} be an integer sequence of length n such that:
a1 = 6
for all 1 ≤ i < n : φ(ai) < φ(ai+1) < ai < ai+11
Let S(N) be the number of such sequences with an ≤ N.
For example, S(10) = 4: {6}, {6, 8}, {6, 8, 9} and {6, 10}.
We can verify that S(100) = 482073668 and S(10 000) mod 108 = 73808307.
Find S(20 000 000) mod 108.
1 φ denotes Euler's totient function.
--hints--
euler337()
should return 85068035.
assert.strictEqual(euler337(), 85068035);
--seed--
--seed-contents--
function euler337() {
return true;
}
euler337();
--solutions--
// solution required