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The recursive sequence generated by the recurrence equation Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), with Q(1)=Q(2)=1. The first few values are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, ... (OEIS ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

The Pell numbers are the numbers obtained by the U_ns in the Lucas sequence with P=2 and Q=-1. They correspond to the Pell polynomial P_n(x) and Fibonacci polynomial F_n(x) ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

The irrational constant R = e^(pisqrt(163)) (1) = 262537412640768743.9999999999992500... (2) (OEIS A060295), which is very close to an integer. Numbers such as the Ramanujan ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

A twin Pythagorean triple is a Pythagorean triple (a,b,c) for which two values are consecutive integers. By definition, twin triplets are therefore primitive triples. Of the ...

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

(dy)/(dx)+p(x)y=q(x)y^n. (1) Let v=y^(1-n) for n!=1. Then (dv)/(dx)=(1-n)y^(-n)(dy)/(dx). (2) Rewriting (1) gives y^(-n)(dy)/(dx) = q(x)-p(x)y^(1-n) (3) = q(x)-vp(x). (4) ...

A boundary value problem is a problem, typically an ordinary differential equation or a partial differential equation, which has values assigned on the physical boundary of ...