3010349

Properties

Appears in sequences

• Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.at n=30A000204
• Associated Mersenne numbers.at n=31A001350
• A Fielder sequence: a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.at n=31A001638
• Bisection of Lucas sequence: a(n) = L(2*n+1).at n=15A002878
• a(n) = 3*a(n-2) - a(n-4), a(0)=0, a(1)=1, a(2)=1, a(3)=4. Alternates Fibonacci (A000045) and Lucas (A000032) sequences for even and odd n.at n=31A005013
• Prime Lucas numbers (cf. A000032).at n=11A005479
• a(n) = floor(phi^n), where phi = (1+sqrt(5))/2 is the golden ratio.at n=31A014217
• Odd Lucas numbers.at n=20A014447
• Incorrect version of A091967.at n=31A031135
• Incorrect version of A107357.at n=31A037181
• a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=7.at n=10A048876
• Smallest primitive prime factor of the n-th Lucas number (A000032); i.e., L(n), L(0) = 2, L(1) = 1 and L(n) = L(n-1) + L(n-2).at n=31A058036
• Primitive part of Lucas(n).at n=30A061447
• Squarefree Lucas numbers.at n=22A063509
• a(n) = Lucas(n) + (-1)^n + 1.at n=30A068397
• Sum of prime factors of Lucas numbers A000032(n),n=0, n>=2, with n=1 term added.at n=31A070827
• Sequence arising from factorization of the Fibonacci numbers.at n=30A072183
• Expansion of (1-2*x)/(1+x-x^2).at n=30A075193
• Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.at n=31A079451
• log_phi(n) is closer to an integer than is log_phi(m) for any m with 2<=m<n, where phi=(1+sqrt(5))/2 is the golden ratio.at n=30A080023