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Rajagopal, A. K.; Uppuluri, V. R. R.; Scott, David S.; Iyengar, S. Sitharama; Yellayi, Mohan

New structural properties of strings generated by leading digits of \(2^ n\). (English) Zbl 0529.60015

Appl. Math. Comput. 14, 221-244 (1984).
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Cited in 2 Documents

MSC:

60E99 Distribution theory
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
82B05 Classical equilibrium statistical mechanics (general)
94A15 Information theory (general)
68R10 Graph theory (including graph drawing) in computer science
11A63 Radix representation; digital problems

Keywords:

first decimal digits of the powers of 2; probabilities of occurrence; state transition graphs; ergodic theory; statistical mechanics
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Full Text: DOI

References:

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[2] Benford, Frank, The law of anomalous numbers, Proc. Amer. Phil. Soc., 78, 551-572 (1938) · Zbl 0018.26502
[3] Raimi, Ralph A., The peculiar distribution of first digits, Scientific American, 221, 109-120 (1969)
[4] Raimi, Ralph A., The first digit problem, Amer. Math. Monthly, 83, 521-538 (1976) · Zbl 0349.60014
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[11] Arnold, V. I.; Avez, A., (Ergodic Problems of Classical Mechanics (1968), Benjamin: Benjamin New York), 134-137, see especially Appendix 12 · Zbl 0167.22901
[12] Pomeau, Y., Stochastic behaviors of simple dynamical systems, (Garrido, L.; Seglar, P.; Shepherd, P. J., Stochastic Processes in Nonequilibrium Systems (1978), Springer: Springer Berlin), 235-277 · Zbl 0351.76082
[13] Kak, S. C.; Chatterjee, A., IEEE Trans. Inform. Theory (Sept. 1981)
[14] Rajagopal, A. K.; Sitharama Iyengar, S.; Yellayi, Mohan, Statistical properties of strings generated by first digits of powers of two, BIT (Sept. 1981), submitted for publication
[15] J. Robertson, V. R. R. Uppuluri, and A. K. Rajapogal, First digit phenomna and ergodic theory, to be submitted to J. Combin. Theory Ser. B.; J. Robertson, V. R. R. Uppuluri, and A. K. Rajapogal, First digit phenomna and ergodic theory, to be submitted to J. Combin. Theory Ser. B. · Zbl 0529.10008
[16] Uppuluri, V. R.R., Essays in Probability and Statistics, 645-650 (1976), Chapter 39 · Zbl 0354.00015
[17] Kak, S. C., New results on the first digit problem, LSU Technical Report EE#607 (Aug. 1981)
[18] Feigenbaum, M. J., Quantitative universality for a class of non-linear transformations, J. Statist. Phys., 19, 25-52 (1978) · Zbl 0509.58037
[19] Feigenbaum, M. J., Universal behavior of non-linear systems, Los Alamos Sci., 4-27 (1980)
[20] S. Sitharama Iyengar, A. K. Rajagopal, and V. R. R. Uppuluri, String patterns of leading digits, J. Appl. Math. and Comp.; S. Sitharama Iyengar, A. K. Rajagopal, and V. R. R. Uppuluri, String patterns of leading digits, J. Appl. Math. and Comp. · Zbl 0513.68036
[21] S. Sitharama Iyengar, A. K. Rajagopal, and Frank Ramos, On the distribution of string sequences of leading digits, J. Comb. Syst. Inf. Theory; S. Sitharama Iyengar, A. K. Rajagopal, and Frank Ramos, On the distribution of string sequences of leading digits, J. Comb. Syst. Inf. Theory · Zbl 0529.60014
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