Density of integer sequences
نویسندگان
چکیده
منابع مشابه
Density of Integer Solutions
Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.
متن کاملGeneralized Nonaveraging Integer Sequences
Let the sequence Sm of nonnegative integers be generated by the following conditions. Set the first term a0 = 0, and for all k ≥ 0, let ak+1 be the least integer greater than ak such that no element of {a0, . . . , ak+1} is the average of m − 1 distinct other elements. Szekeres gave a closed-form description of S3 in 1936, and Layman provided a similar description for S4 in 1999. We first find ...
متن کاملMy Favorite Integer Sequences
This paper gives a brief description of the author’s database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Many unsolved problems are mentioned. This paper was published (in a somewhat different form) in Sequences and their Applications (Proceedings of SETA ’98), C. Ding, T. Helleseth and H. Niederreiter (editors...
متن کاملAutomatic Invention of Integer Sequences
We report on the application of the HR program (Colton, Bundy, & Walsh 1999) to the problem of automatically inventing integer sequences. Seventeen sequences invented by HR are interesting enough to have been accepted into the Encyclopedia of Integer Sequences (Sloane 2000) and all were supplied with interesting conjectures about their nature, also discovered by HR. By extending HR, we have ena...
متن کاملInteger Sequences and Periodic Points
Arithmetic properties of integer sequences counting periodic points are studied, and applied to the case of linear recurrence sequences, Bernoulli numerators, and Bernoulli denominators.
متن کاملذخیره 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: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0236141-3