A theorem of Ljunggren and Jacobsthal on Bernoulli numbers

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New families of Jacobsthal and Jacobsthal-Lucas numbers

In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. Introduction Several sequences of positive integers were and still are object of study for many researchers. Examples of these sequences are the well known Fibonacci ...

متن کامل

A New Generalization of Jacobsthal Numbers (bi-periodic Jacobsthal Sequences)

The bi-periodic Fibonacci sequence also known as the generalized Fibonacci sequence was fırst introduced into literature in 2009 by Edson and Yayenie [9] after which the bi-periodic Lucas sequence was defined in a similar fashion in 2004 by Bilgici [5]. In this study, we introduce a new generalization of the Jacobsthal numbers which we shall call bi-periodic Jacobsthal sequences similar to the ...

متن کامل

On Lucas-bernoulli Numbers

In this article we investigate the Bernoulli numbers B̂n associated to the formal group laws whose canonical invariant differentials generate the Lucas sequences {Un} and {Vn}. We give explicit expressions for these numbers and prove analogues of Kummer congruences for them.

متن کامل

On Some Identities of k-Jacobsthal-Lucas Numbers

In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83

متن کامل

Ternary Modified Collatz Sequences And Jacobsthal Numbers

We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1954

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1954-0059298-6