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The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...

The Möbius function is a number theoretic function defined by mu(n)={0 if n has one or more repeated prime factors; 1 if n=1; (-1)^k if n is a product of k distinct primes, ...

Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative ...

An n-digit number that is the sum of the nth powers of its digits is called an n-narcissistic number. It is also sometimes known as an Armstrong number, perfect digital ...

Call a number of the form n^2-k a "near-square number." Numbers of the form n^2-5 for n=1, 2, ... are -4, -1, 4, 11, 20, 31, 44, 59, 76, 95, ... (OEIS A028875). These are ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

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 ...

The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...