Geodesic
On an expansion real numbers on some sequences
Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 50-60

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In this paper theorems on the expression of real numbers on multiplicative number system, Fibonacci sequence and integral valued sequences satisfiing recurrent correlations and connected with Pisot–Vidgajraghavan, are proven. It pay a special attention to “explicit formulas” and conditions of the uniqueness of such representations. We note that unifiing of an expression of a real number over inverse values of a multiplicaticative system permits to get the estimation of the form $$ e-\sum_{k=0}^n\frac 1{k!}=\frac{x_n}{n!}, \frac 1{n+1}\leq x_n\frac 1n. $$ Expressions of numbers over the sequence of inverse of Fibonacci numbers essentially uses these representation throw powers of “the gold section” $\varphi=\frac{1+\sqrt 5}{2}.$ Systems numbers connected with Pisot–Vidgajraghavana were considered less than in details, as demands to make a properties of examinated numbers more concrete.
Keywords: multiplicative number system, the Fibonacci's sequence. 
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     title = {On an expansion real numbers on some sequences},
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A. K. Giyasi; I. P. Mikhailov; V. N. Chubarikov. On an expansion real numbers on some sequences. Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 50-60. http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a3/