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We consider two quantities that measure complexity of binary strings:$\mathit{KA}(x)$ is defined as the minus logarithm of continuous a prioriprobability on the binary tree, and $\mathit{KP}(x)$ denotes prefix complexityof a binary string $x$. In this paper we answer a question posed by JosephMiller and prove that there exists an infinite binary sequence $\omega$ suchthat the sum of $2^{\mathit{KA}(x)-\mathit{KP}(x)}$ over all prefixes $x$ of$\omega$ is infinite. Such a sequence can be chosen among characteristicsequences of computably enumerable sets.

The sum $2^{\mathit{KA}(x)-\mathit{KP}(x)}$ over all prefixes $x$ of some binary sequence can be infinite