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A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the ...

The Leibniz harmonic triangle is the number triangle given by 1/11/2 1/21/3 1/6 1/31/4 1/(12) 1/(12) 1/41/5 1/(20) 1/(30) 1/(20) 1/5 (1) (OEIS A003506), where each fraction ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

The abundancy of a number n is defined as the ratio sigma(n)/n, where sigma(n) is the divisor function. For n=1, 2, ..., the first few values are 1, 3/2, 4/3, 7/4, 6/5, 2, ...