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A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758 Extravagant numbers
1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2 ...
As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction 5 / 7 when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...
11.1 Mathematics. 11.2 ... In mathematics, the Fibonacci sequence is a sequence in which each term is ... which is F n−1, plus the number of male ancestors ...
In mathematics, a sequence is an enumerated collection of ... [1] [2] Sequences are useful in a number of mathematical ... 11, 13, 17, ...). The prime numbers are ...
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms. Exponential function [ edit ]
In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that. The first few terms of the sequence are 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, … (sequence A000129 in the OEIS).
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