Integer sequence

Encyclopedia : I : IN : INT : Integer sequence

---

In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.

An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula n² − 1 for the nth term: an explicit definition.

Integer sequences which have received their own name include:

• Abundant numbers
• Bell numbers
• Binomial coefficients
• Carmichael numbers
• Catalan numbers
• Composite numbers
• Deficient numbers
• Euler numbers
• Even and odd numbers
• Factorial numbers
• Fibonacci numbers
• Figurate numbers
• Happy numbers
• Highly totient numbers
• Highly composite numbers
• Hyperperfect numbers
• Lucky numbers
• Lucas numbers
• Perfect numbers
• Pseudoperfect numbers
• Prime numbers
• Pseudoprime numbers
• Semiperfect numbers
• Semiprime numbers
• Weird numbers

An integer sequence is a computable sequence, if there exists an algorithm which given n, calculates a_n, for all n > 0. An integer sequence is a definable sequence, if there exists some statement P(x) which is true for that integer sequence x and false for all other integer sequences. The set of computable integer sequences and definable integer sequences are both countable, with the computable sequences a proper subset of the definable sequences. The set of all integer sequences is uncountable; thus, almost all integer sequences are uncomputable and cannot be defined.

See also

• On-Line Encyclopedia of Integer Sequences

External links

• [Journal of Integer Sequences]. Articles are freely available online.

 

---

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.

Search Titles

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

?