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Catalan (1876, 1891) noted that the sequence of Mersenne numbers 2^2-1=3, 2^3-1=7, and 2^7-1=127, and (OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the ...

Based on methods developer in collaboration with M. Leclert, Catalan (1865) computed the constant K=0.915965594177... (OEIS A006752) now known as Catalans' constant to 9 ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

Approximations to Catalan's constant include K approx (9/(10))^(5/6) (1) approx ln(ln892)-1 (2) approx (1/(96))^(1/52) (3) approx (4/(51))^(1/29) (4) approx ...

The simple continued fraction representations for Catalan's constant K is [0, 1, 10, 1, 8, 1, 88, 4, 1, 1, ...] (OEIS A014538). A plot of the first 256 terms of the continued ...

A minimal surface given by the parametric equations x(u,v) = u-sinucoshv (1) y(u,v) = 1-cosucoshv (2) z(u,v) = 4sin(1/2u)sinh(1/2v) (3) (Gray 1997), or x(r,phi) = ...

The conjecture that there are only finitely many triples of relatively prime integer powers x^p, y^q, z^r for which x^p+y^q=z^r (1) with 1/p+1/q+1/r<1. (2) Darmon and Merel ...

Special cases of general formulas due to Bessel. J_0(sqrt(z^2-y^2))=1/piint_0^pie^(ycostheta)cos(zsintheta)dtheta, where J_0(z) is a Bessel function of the first kind. Now, ...

Clark's triangle is a number triangle created by setting the vertex equal to 0, filling one diagonal with 1s, the other diagonal with multiples of an integer f, and filling ...

The triangle DeltaA^*B^*C^* obtained by reflecting the vertices of a reference triangle DeltaABC about the opposite sides is called the reflection triangle (Grinberg 2003). ...