## GCD sequence

### Problem 443

Published on Saturday, 2nd November 2013, 04:00 pm; Solved by 474; Difficulty rating: 30%Let g(`n`) be a sequence defined as follows:

g(4) = 13,

g(`n`) = g(`n`-1) + gcd(`n`, g(`n`-1)) for `n` > 4.

The first few values are:

n | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | ... |

g(n) | 13 | 14 | 16 | 17 | 18 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 51 | 54 | 55 | 60 | ... |

You are given that g(1 000) = 2524 and g(1 000 000) = 2624152.

Find g(10^{15}).