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A number that has fewer digits than the number of digits in its prime factorization (including exponents). A046760: Pandigital numbers: 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ... Numbers containing the digits 0–9 such that each digit appears exactly once. A050278
Pascal's triangle, rows 0 through 7. The number of odd integers in row i is the i-th number in Gould's sequence. The self-similar sawtooth shape of Gould's sequence. Gould's sequence is an integer sequence named after Henry W. Gould that counts how many odd numbers are in each row of Pascal's triangle. It consists only of powers of two, and ...
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.
Even and odd numbers: An integer is even if it is a multiple of 2, and is odd otherwise. Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
If one considers only the odd numbers in the sequence generated by the Collatz process, then each odd number is on average 3 / 4 of the previous one. [16] (More precisely, the geometric mean of the ratios of outcomes is 3 / 4 .) This yields a heuristic argument that every Hailstone sequence should decrease in the long run ...
Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number , (sequence A000396 in the OEIS ), even though we do not have a formula for the n th perfect number.
Printable version; In other projects ... This is the first number of the sequence. ... In the case of n = 23, since n is an odd number that is not a multiple of 3, ...
Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...
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