Fibonacci
... in terms of α itself. Then do the same for β. 20. What proportion of the Fibonacci numbers are even? What fraction of them are multiples of 3? multiples of 4? 5? Is there a pattern to these answers? I read this problem at Jim Tanton’s webpage. 21. The first four terms of a sequence are 2, 6, 12, 72. ...
... in terms of α itself. Then do the same for β. 20. What proportion of the Fibonacci numbers are even? What fraction of them are multiples of 3? multiples of 4? 5? Is there a pattern to these answers? I read this problem at Jim Tanton’s webpage. 21. The first four terms of a sequence are 2, 6, 12, 72. ...
On certain positive integer sequences (**)
... ones in their binary expansion. D e f i n i t i o n 1. Let k F 2 , l F 1 , m F 2 be positive integers. We say that a positive integer n is a (k , l , m)-number if the sum of digits of n m in its expansion in base k is l times the sum of the digits of the expansion in base k of n . The above sequence ...
... ones in their binary expansion. D e f i n i t i o n 1. Let k F 2 , l F 1 , m F 2 be positive integers. We say that a positive integer n is a (k , l , m)-number if the sum of digits of n m in its expansion in base k is l times the sum of the digits of the expansion in base k of n . The above sequence ...
"The Asymptotic Equipartition Property". In: Elements of Information
... short descriptions for such sequences of random variables. We divide all sequences in 2” into two sets: the typical set A:’ and its complement, as shown in Figure 3.1. We order all elements in each set according to some order (say lexicographic order). Then we can represent each sequence of A:’ by g ...
... short descriptions for such sequences of random variables. We divide all sequences in 2” into two sets: the typical set A:’ and its complement, as shown in Figure 3.1. We order all elements in each set according to some order (say lexicographic order). Then we can represent each sequence of A:’ by g ...
PPT
... a procedure that calls itself • This is often convenient but we must make sure that the recursion eventually terminates – Have a base case (here r=l) – Reduce some parameter in each call (here r-l) ...
... a procedure that calls itself • This is often convenient but we must make sure that the recursion eventually terminates – Have a base case (here r=l) – Reduce some parameter in each call (here r-l) ...
![[Part 1]](http://s1.studyres.com/store/data/008795788_1-6323173b144ce5752d9cfa6a3116d3f8-300x300.png)
sequence
... You can also write an algebraic expression to represent the relationship between any term in a sequence an its position in the sequence. ...
... You can also write an algebraic expression to represent the relationship between any term in a sequence an its position in the sequence. ...
Exploring Fibonacci Numbers using a spreadsheet
... (which is approximately equal to 1.618 up to three decimal places). ...
... (which is approximately equal to 1.618 up to three decimal places). ...
Sequence
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them into computer memory; infinite sequences are also called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.