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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 ...
Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...
The lazy caterer's sequence (green) and other OEIS sequences in Bernoulli's triangle. As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the lazy caterer's sequence for n cuts, where n ≥ 2. The sequence can be alternatively derived from the sum of up to the first 3 terms of each row of Pascal's ...
For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...
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In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser 's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = , giving the sequence 1, 2, 4 ...
August 12, 2024 at 2:13 PM. Grace Kerber is the 23-year-old mastermind behind Mohawk Chevrolet’s “The Dealership.”. If you’re eagerly awaiting the release of “The Office” spinoff, this ...
A constant-recursive sequence is any sequence of integers, rational numbers, algebraic numbers, real numbers, or complex numbers (written as as a shorthand) satisfying a formula of the form. for all for some fixed coefficients ranging over the same domain as the sequence (integers, rational numbers, algebraic numbers, real numbers, or complex ...