The objective decision whether a given sequence consists of random or of non-random numbers is not easy, but Kolmogorov published (in Italian) a paper on this problem in an insurance statistics journal (G. ist. ital. attar. 1933). The randomness measure introduced in that paper suggests that the geometric progressions like 03, 09, 27, 81, 43, 29, 87, 61, 83, 49, 47, 41, 23, 69, 07 are more random than the arithmetical ones like 37, 74, 11, 48, 85, 22, 59, 96, 33, 70, 07, 44, 81, 18, 55. For the arithmetical progressions of fractional parts, whose difference is a rational number, the randomness parameter tends to zero when the length of the progression grows. There exist irrational differences for which the randomness parameters of long arithmetical progressions of fractional parts do not tend to zero and whose behaviour is unknown for almost all values of the difference because of some unsolved problems of the statistics of continued fractions. The most known use of the Kolmogorov Italian paper to practical problems was his 1940 study of the attempts by Lyzenko to reject the Mendel law of genetics, which was based on the empirically observed difference between the experimental data and the prediction of Mendel's law. Kolmogorov proved that the experiences of the Lyzenko school confirmed the Mendel law rather than reject it: a smaller difference between the theory and the experiment would be a proof of the falsification of the experimental data. These conclusions of Kolmogorov were, however, unpublished, since the classical genetic experts answered to Lyzenko by their own experimental data, whose difference with Mendel's prediction were minimal.