Notes on finding the Nth term in sequences using factoring
... But this doesn't seem to be too helpful. There is a pattern, but it appears to alternate (one pattern with odd terms end another with even terms). H factoring doesn't help, it may be because the formula involves division as well as factoring. If you suspect that the rule involves division, try doubl ...
... But this doesn't seem to be too helpful. There is a pattern, but it appears to alternate (one pattern with odd terms end another with even terms). H factoring doesn't help, it may be because the formula involves division as well as factoring. If you suspect that the rule involves division, try doubl ...
Lecture 3
... In many computer applications we need to use random numbers, something which can be seen as a toss of a coin or a throw of a die. Pseudorandom Numbers: numbers that look random. A linear congruential method for generating pseudorandom numbers : ...
... In many computer applications we need to use random numbers, something which can be seen as a toss of a coin or a throw of a die. Pseudorandom Numbers: numbers that look random. A linear congruential method for generating pseudorandom numbers : ...
Recurrence relations and generation functions
... Determine the number of ways to color the squares of a 1-by-n chessboard, usign the colors red, white, and blue, if an even number of squares are to be colored red. Hints: Let hn denote the number of such colorings where we define h0 =1. Then hn equals tgeh number of n-permutations of a multiset of ...
... Determine the number of ways to color the squares of a 1-by-n chessboard, usign the colors red, white, and blue, if an even number of squares are to be colored red. Hints: Let hn denote the number of such colorings where we define h0 =1. Then hn equals tgeh number of n-permutations of a multiset of ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.