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The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...

The Fibonacci number F_(n+1) gives the number of ways for 2×1 dominoes to cover a 2×n checkerboard, as illustrated in the diagrams above (Dickau). The numbers of domino ...

A prime power is a prime or integer power of a prime. A test for a number n being a prime is implemented in the Wolfram Language as PrimePowerQ[n]. The first few prime powers ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Let a prime number generated by Euler's prime-generating polynomial n^2+n+41 be known as an Euler prime. (Note that such primes are distinct from prime Euler numbers, which ...

Honaker's problem asks for all consecutive prime number triples (p,q,r) with p<q<r such that p|(qr+1). Caldwell and Cheng (2005) showed that the only Honaker triplets for ...

An ordinal number is called an initial ordinal if every smaller ordinal has a smaller cardinal number (Moore 1982, p. 248; Rubin 1967, p. 271). The omega_alphas ordinal ...

The representation, beloved of engineers and physicists, of a complex number in terms of a complex exponential x+iy=|z|e^(iphi), (1) where i (called j by engineers) is the ...

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...

As proved by Sierpiński (1960), there exist infinitely many positive odd numbers k such that k·2^n+1 is composite for every n>=1. Numbers k with this property are called ...