Statistical analysis of the first digits of the binary expansion of Feigenbaum constants α and δ

We present a detailed statistical analysis of the blocks appearing in the binary expansions of the Feigenbaum constants α and δ for the logistic map. Significant deviations from randomness are revealed, suggesting that these constants correspond to non-normal binary numbers. Applying a widely believed conjecture, it is concluded that the transcendental character of the constants can be seriously envisaged, within the limits of the statistical precision corresponding to the number of digits available.