id	title	challengeType	forumTopicId	dashedName
5900f53c1000cf542c51004e	Problem 463: A weird recurrence relation	5	302138	problem-463-a-weird-recurrence-relation

--description--

The function f is defined for all positive integers as follows:

f(1)=1

f(3)=3

f(2n)=f(n)

f(4n + 1)=2f(2n + 1) - f(n)

f(4n + 3)=3f(2n + 1) - 2f(n)

The function S(n) is defined as \\sum\_{i=1}^{n}f(i). S(8)=22 and S(100)=3604. Find S(3^{37}). Give the last 9 digits of your answer.

--hints--

euler463() should return 808981553.

assert.strictEqual(euler463(), 808981553);

function euler463() {

  return true;
}

euler463();

// solution required