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A number of the form 2^n-1 obtained by setting x=1 in a Fermat-Lucas polynomial, more commonly known as a Mersenne number.

The two recursive sequences U_n = mU_(n-1)+U_(n-2) (1) V_n = mV_(n-1)+V_(n-2) (2) with U_0=0, U_1=1 and V_0=2, V_1=m, can be solved for the individual U_n and V_n. They are ...

An n-step Lucas sequence {L_k^((n))}_(k=1)^infty is defined by letting L_k^((n))=-1 for k<0, L_0^((n))=n, and other terms according to the linear recurrence equation ...

The first few prime Lucas numbers L_n are 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, ... (OEIS A005479), corresponding to indices n=0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 31, ...

A sequence which arises in the hypothetical reproduction of a population of rabbits. Let the substitution system map 0->1 correspond to young rabbits growing old, and 1->10 ...

The golden ratio conjugate, also called the silver ratio, is the quantity Phi = 1/phi (1) = phi-1 (2) = 2/(1+sqrt(5)) (3) = (sqrt(5)-1)/2 (4) = 0.6180339887... (5) (OEIS ...

The heptanacci constant is the limiting ratio of adjacent heptanacci numbers. It is the algebraic number P = (x^7-x^6-x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.99196419660... (2) (OEIS ...

The hexanacci constant is the limiting ratio of adjacent hexanacci numbers. It is the algebraic number P = (x^6-x^5-x^4-x^3-x^2-x-1)_2 (1) = 1.98358284342... (2) (OEIS ...

The pentanacci constant is the limiting ratio of adjacent pentanacci numbers. It is the algebraic number P = (x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.96594823... (2) (OEIS A103814), ...

As originally stated by Gould (1972), GCD{(n-1; k),(n; k-1),(n+1; k+1)} =GCD{(n-1; k-1),(n; k+1),(n+1; k)}, (1) where GCD is the greatest common divisor and (n; k) is a ...