103681

Properties

Appears in sequences

• a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 2.at n=23A001610
• a(n) = F(2n+1) + F(2n-1) - 1.at n=12A005592
• a(n) = floor(phi^n), where phi = (1+sqrt(5))/2 is the golden ratio.at n=24A014217
• a(i) is a square mod a(j), i <> j; a(n) prime; a(1) = 2.at n=11A034902
• Shifts left two places under BIN1 transform.at n=24A052341
• 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=36A058036
• Primitive part of Lucas(n).at n=35A061447
• Cyclotomic polynomials Phi_n at x=phi, ceiled up (where phi = tau = (sqrt(5)+1)/2).at n=23A063707
• Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.at n=36A079451
• Order in which prime factors first occur in the Lucas sequence.at n=40A096362
• a(n) = Fibonacci(n-1) + Fibonacci(n+1) - (-1)^n.at n=24A098600
• Triangle, read by rows, of the coefficients of [x^k] in G100231(x)^n such that the row sums are 5^n-1 for n>0, where G100231(x) is the g.f. of A100231.at n=44A100232
• a(n) = Lucas(3*n) - 1.at n=8A100233
• Primes of the form 512n+257.at n=33A105131
• a(n) = L(3*n)/L(n), where L(n) = Lucas number.at n=12A110391
• Least k such that k*p(n)#/5-3+j is prime for j=2,4,8.at n=41A111122
• Primes that are the difference of two Lucas numbers; primes in A113191.at n=31A113192
• Primes corresponding to the indices of A059791.at n=8A118839
• Numbers that are the sum of exactly two sets of Fibonacci numbers.at n=42A122194
• Primes of the form 5k^2 + 1.at n=8A137530