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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 ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
1,3,3-Trinitroazetidine ( TNAZ) is an explosive heterocyclic compound that has been considered as a potential replacement for TNT because of its low melting point (101 °C) and good thermal stability (up to 240 °C). TNAZ was first synthesized by Archibald et al. in 1990. [3]
Fibonacci sequence. For the chamber ensemble, see Fibonacci Sequence (ensemble). 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 ...
President Barack Obama behind the wheel of a new Chevrolet Volt during his tour of the General Motors Auto Plant in Hamtramck, Michigan in 2010. In his 2011 State of the Union address, President Barack Obama set the goal for the U.S. to become the first country to have one million electric vehicles on the road by 2015. [20]
The Braves finished the first half 53-42 and in second place in the NL East, 8 1/2 games behind the Philadelphia Philli d'Arnaud hits two homers, drives in 4 runs in Atlanta 6-3 win over San Diego ...
t. e. The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...
The threefold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 3 + 6 − 10 + ..., the alternating series of triangular numbers; its Abel and Euler sum is 1 ⁄ 8. [16] The fourfold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 4 + 10 − 20 + ..., the alternating series of tetrahedral numbers , whose Abel sum is 1 ⁄ 16 .