freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-463-a-weird-recurrence-relation.english.md

id, challengeType, isHidden, title, forumTopicId

id	challengeType	isHidden	title	forumTopicId
5900f53c1000cf542c51004e	5	false	Problem 463: A weird recurrence relation	302138

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.

Instructions

Tests

tests:
  - text: <code>euler463()</code> should return 808981553.
    testString: assert.strictEqual(euler463(), 808981553);

Challenge Seed

function euler463() {
  // Good luck!
  return true;
}

euler463();

Solution

// solution required