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A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

The determination of the number of monotone Boolean functions of n variables (equivalent to the number of antichains on the n-set {1,2,...,n}) is called Dedekind's problem, ...

The imaginary part I[z] of a complex number z=x+iy is the real number multiplying i, so I[x+iy]=y. In terms of z itself, I[z]=(z-z^_)/(2i), where z^_ is the complex conjugate ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a heptagonal number H_n and pentagonal number P_m. Such numbers exist when 1/2n(5n-3)=1/2m(3m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a heptagonal number H_n and square number S_m. Such numbers exist when 1/2n(5n-3)=m^2. (1) Completing the square and rearranging gives ...

A composite number defined analogously to a Smith number except that the sum of the number's digits equals the sum of the digits of its distinct prime factors (excluding 1). ...

Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. Now sum the two and ...

A number which is simultaneously a pentagonal number P_n and a square number S_m. Such numbers exist when 1/2n(3n-1)=m^2. (1) Completing the square gives ...

A Poulet number is a Fermat pseudoprime to base 2, denoted psp(2), i.e., a composite number n such that 2^(n-1)=1 (mod n). The first few Poulet numbers are 341, 561, 645, ...