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A graph whose nodes are sequences of symbols from some alphabet and whose edges indicate the sequences which might overlap. The above figures show the first few n-dimensional ...

The probability of getting at least one "6" in four rolls of a single 6-sided die is 1-(5/6)^4 approx 0.5177, (1) which is slightly higher than the probability of at least ...

e^(i(ntheta))=(e^(itheta))^n. (1) From the Euler formula it follows that cos(ntheta)+isin(ntheta)=(costheta+isintheta)^n. (2) A similar identity holds for the hyperbolic ...

Let union represent "or", intersection represent "and", and ^' represent "not." Then, for two logical units E and F, (E union F)^'=E^' intersection F^' (E intersection ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

de Rham's function is the function defined by the functional equations phi_alpha(1/2x) = alphaphi_alpha(x) (1) phi_alpha(1/2(x+1)) = alpha+(1-alpha)phi_alpha(x) (2) (Trott ...

The constants C_n defined by C_n=[int_0^infty|d/(dt)((sint)/t)^n|dt]-1. (1) These constants can also be written as the sums C_n=2sum_(k=1)^infty(1+x_k^2)^(-n/2), (2) and ...

A number n is called an e-perfect number if sigma_e(n)=2n, where sigma_e(n) is the sum of the e-Divisors of n. If m is squarefree, then sigma_e(m)=m. As a result, if n is ...

An amazing pandigital approximation to e that is correct to 18457734525360901453873570 decimal digits is given by (1+9^(-4^(7·6)))^(3^(2^(85))), (1) found by R. Sabey in 2004 ...

The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...