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On the sum of digits of some sequences of integers

100%

Cilleruelo J., Luca F., Rué J., Zumalacárregui A.

Open Mathematics

2013

tom 11

nr 1

188-195

Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.

Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions

51%

Mező I.

Open Mathematics

2013

tom 11

nr 5

931-939

There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli, Gosper and Srivastava. In this paper, we extend some of them. Namely, we give the exponential generating function of hyperharmonic numbers indexed by arithmetic progressions; in the sum several combinatorial numbers (like Stirling and Bell numbers) and the hypergeometric function appear.

Ograniczanie wyników

2 Open Mathematics

1 Cilleruelo J.

1 Luca F.

1 Mező I.

1 Rué J.

1 Zumalacárregui A.

2 2013

Wyniki wyszukiwania

On the sum of digits of some sequences of integers

Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions