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Leonhard Euler published the polynomial k 2 − k + 41 which produces prime numbers for all integer values of k from 1 to 40. Only 6 lucky numbers of Euler exist, namely 2, 3, 5, 11, 17 and 41 (sequence A014556 in the OEIS). [1] Note that these numbers are all prime numbers. The primes of the form k 2 − k + 41 are
Continue removing the nth remaining numbers, where n is the next number in the list after the last surviving number. Next in this example is 9. One way that the application of the procedure differs from that of the Sieve of Eratosthenes is that for n being the number being multiplied on a specific pass, the first number eliminated on the pass is the n-th remaining number that has not yet been ...
17 is a Leyland number [3] and Leyland prime, [4] using 2 & 3 (2 3 + 3 2) and using 4 and 5, [5] [6] using 3 & 4 (3 4 - 4 3). 17 is a Fermat prime. 17 is one of six lucky numbers of Euler. [7] Since seventeen is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler.
1, 2, and 3 are not of the required form, so the Heegner numbers that work are 7, 11, 19, 43, 67, 163, yielding prime generating functions of Euler's form for 2, 3, 5, 11, 17, 41; these latter numbers are called lucky numbers of Euler by F. Le Lionnais. [4]
In mathematics, the Euler numbers are a sequence E n of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion = + = =!, where is the hyperbolic cosine function.
Euler's number, e = 2.71828 . . . , the base of the natural logarithm; Euler's idoneal numbers, a set of 65 or possibly 66 or 67 integers with special properties; Euler numbers, integers occurring in the coefficients of the Taylor series of 1/cosh t; Eulerian numbers count certain types of permutations.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
A totient number is a value of Euler's totient function: that is, an m for which there is at least one n for which φ(n) = m. The valency or multiplicity of a totient number m is the number of solutions to this equation. [40] A nontotient is a natural number which is not a totient number. Every odd integer exceeding 1 is trivially a nontotient.