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0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add" : a (0) = 0; for n > 0, a ( n ) = a ( n − 1) − n if that number is positive and not already in the sequence, otherwise a ( n ) = a ( n − 1) + n , whether or not that number is already in the sequence.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. 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.
122 is a nontotient since there is no integer with exactly 122 coprimes below it. Nor is there an integer with exactly 122 integers with common factors below it, making 122 a noncototient. 122 is a semiprime. 122 is the sum of squares of the divisors of 11. φ(122) = φ(σ(122)). [1]
Plot of the first 10,000 Pisano periods. In number theory, the nth Pisano period, written as π (n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats.
This accounts for 0.7% of all American households that have a pet. But for rabbit owners and prospective ones, you may wonder how long your furry companion will live. Their lifespan varies ...
U.S. smoking rates have fallen dramatically in the past six decades, from 42.6% of American adults in 1965 to 11.6% in 2022, according to the American Lung Association. But, according to the U.S ...
December 16, 2024 at 7:00 AM. The Washington Post argued in a new editorial that the benefits of gender-transition treatments for minors like puberty blockers have not been scientifically proven.
The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯.The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...