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Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
The Hofstadter Q sequence is defined as follows: [3] [7] = =, = (()) + (()), >The first few terms of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9 ...
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
Oxidation of hydrocarbons (unburnt and partially burned fuel) to carbon dioxide and water: C x H 2x+2 + [(3x+1)/2]O 2 → xCO 2 + (x+1)H 2 O (a combustion reaction) The two-way catalytic converter is widely used on diesel engines to reduce hydrocarbon and carbon monoxide emissions. They were also used on gasoline engines in American and ...
3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1. The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part.
Semi-log plot of solutions of + + = for integer , , and , and .Green bands denote values of proven not to have a solution.. In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum.
The Hundred Fowls Problem as presented in Zhang Qiujian suanjing can be translated as follows: [4] "Now one cock is worth 5 qian, one hen 3 qian and 3 chicks 1 qian. It is required to buy 100 fowls with 100 qian.