Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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.

Comments on the height reducing property

64%

Akiyama S., Zaimi T.

Open Mathematics

2013

tom 11

nr 9

1616-1627

A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus greater than one. Expecting the converse of the last statement is true, we show some theoretical and experimental results, which support this conjecture.

Ograniczanie wyników

2 Open Mathematics

1 Akiyama S.

1 Cilleruelo J.

1 Luca F.

1 Rué J.

1 Zaimi T.

1 Zumalacárregui A.

2 2013

Wyniki wyszukiwania

On the sum of digits of some sequences of integers

Comments on the height reducing property