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Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

The disorder number of a simple connected graph on n vertices is defined as the maximum length of a walk along the edges of the graph taken over all ordering of its vertices ...

The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-bridge knots. There is a one-to-one ...

The rook numbers r_k^((m,n)) of an m×n board are the number of subsets of size k such that no two elements have the same first or second coordinate. In other word, it is the ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

An odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic ...

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

A tetradic (or four-way) number is a number that remains unchanged when flipped back to front, mirrored up-down, or flipped up-down. Since the only numbers that remain ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

A number n is called an economical number if the number of digits in the prime factorization of n (including powers) uses fewer digits than the number of digits in n. The ...