{"app":{"locale":"en-GB"},"problem":{"content":"

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

\\[\\begin{matrix}n & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & \\ldots \\\\G(n) & 1 & 2 & 2 & 3 & 3 & 4 & 4 & 4 & 5 & 5 & 5 & 6 & 6 & 6 & 6 & \\ldots\\end{matrix}\\]

You are given that $G(10^3) = 86$, $G(10^6) = 6137$.
You are also given that $\\sum G(n^3) = 153506976$ for $1 \\le n \\lt 10^3$.

Find $\\sum G(n^3)$ for $1 \\le n \\lt 10^6$.

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