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The complementary Bell numbers, also called the Uppuluri-Carpenter numbers, B^~_n=sum_(k=0)^n(-1)^kS(n,k) (1) where S(n,k) is a Stirling number of the second kind, are ...

A Cullen number is a number of the form C_n=2^nn+1. The first few are 3, 9, 25, 65, 161, 385, ... (OEIS A002064). Cullen numbers are divisible by p=2n-1 if p is a prime of ...

A plane path on a set of equally spaced lattice points, starting at the origin, where the first step is one unit to the north or south, the second step is two units to the ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

The problem of determining how many nonattacking knights K(n) can be placed on an n×n chessboard. For n=8, the solution is 32 (illustrated above). In general, the solutions ...

Li's criterion states that the Riemann hypothesis is equivalent to the statement that, for lambda_n=1/((n-1)!)(d^n)/(ds^n)[s^(n-1)lnxi(s)]|_(s=1), (1) where xi(s) is the ...

A McNugget number is a positive integer that can be obtained by adding together orders of McDonald's® Chicken McNuggetsTM (prior to consuming any), which originally came in ...

Mills' theorem states that there exists a real constant A such that |_A^(3^n)_| is prime for all positive integers n (Mills 1947). While for each value of c>=2.106, there are ...

The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...

A phi-prime is a prime number appearing in the decimal expansion of the golden ratio phi. The first few are 1618033, 1618033988749, ... (OEIS A064117). The numbers of decimal ...