54018521

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=36A000204
• Associated Mersenne numbers.at n=37A001350
• A Fielder sequence: a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.at n=37A001638
• a(n) = Lucas(5*n+2).at n=7A001947
• Bisection of Lucas sequence: a(n) = L(2*n+1).at n=18A002878
• 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=37A005013
• Prime Lucas numbers (cf. A000032).at n=12A005479
• a(n) = floor(phi^n), where phi = (1+sqrt(5))/2 is the golden ratio.at n=37A014217
• Odd Lucas numbers.at n=24A014447
• a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=7.at n=12A048876
• a(n) = Lucas(4*n+1).at n=9A056914
• 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=37A058036
• Primitive part of Lucas(n).at n=36A061447
• Squarefree Lucas numbers.at n=27A063509
• a(n) = Lucas(n) + (-1)^n + 1.at n=36A068397
• Sum of prime factors of Lucas numbers A000032(n),n=0, n>=2, with n=1 term added.at n=37A070827
• Sequence arising from factorization of the Fibonacci numbers.at n=36A072183
• Expansion of (1-2*x)/(1+x-x^2).at n=36A075193
• Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.at n=37A079451
• 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=36A080023