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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.

Fourier series of functions involving higher-order ordered Bell polynomials

76%

Kim T., Kim D. S., Jang G.-W., Jang L. C.

Open Mathematics

2017

tom 15

nr 1

1606-1617

In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.

Ograniczanie wyników

2 Open Mathematics

1 Cilleruelo J.

1 Jang G.-W.

1 Jang L. C.

1 Kim D. S.

1 Kim T.

1 Luca F.

1 Rué J.

1 Zumalacárregui A.

1 2017

1 2013

Wyniki wyszukiwania

On the sum of digits of some sequences of integers

Fourier series of functions involving higher-order ordered Bell polynomials