On sequences of solid type. (English) Zbl 0769.11013
Probability theory and applications, Essays to the Mem. of J. Mogyoródi, Math. Appl. 80, 335-342 (1992).
[For the entire collection see Zbl 0755.00022.]
A real sequence \((a_ n)\) is said to be of solid type if there exists a sequence \(s: \mathbb{N}\to\mathbb{N}\backslash\{1\}\) such that \(a_ n=a_{n+1}+a_{n+2}+\cdots+ a_{n+s(n)}\) for any \(n\in\mathbb{N}\). The authors prove some results concerning such sequences and interval-filling sequences, introduced by Z. Daróczy, A. Járai and I. Kátai [Acta Sci. Math. 50, 337-350 (1986; Zbl 0619.10007)].
A real sequence \((a_ n)\) is said to be of solid type if there exists a sequence \(s: \mathbb{N}\to\mathbb{N}\backslash\{1\}\) such that \(a_ n=a_{n+1}+a_{n+2}+\cdots+ a_{n+s(n)}\) for any \(n\in\mathbb{N}\). The authors prove some results concerning such sequences and interval-filling sequences, introduced by Z. Daróczy, A. Járai and I. Kátai [Acta Sci. Math. 50, 337-350 (1986; Zbl 0619.10007)].
Reviewer: L.Tóth (Cluj)
MSC:
| 11B83 | Special sequences and polynomials |
| 11A63 | Radix representation; digital problems |
| 40A05 | Convergence and divergence of series and sequences |
| 26A30 | Singular functions, Cantor functions, functions with other special properties |
