Problem 341
Golomb's self-describing sequence

The Golomb's self-describing sequence {G(n)} is the only nondecreasing sequence of natural numbers such that n appears exactly G(n) times in the sequence. The values of G(n) for the first few n are

n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
G(n) 1 2 2 3 3 4 4 4 5 5 5 6 6 6 6

You are given that G(103) = 86, G(106) = 6137.
You are also given that ΣG(n3) = 153506976 for 1 ≤n < 103.

Find ΣG(n3) for 1 ≤n < 106.

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http://projecteuler.net/problem=341