19489

Properties

Appears in sequences

• a(n) = 1 + C(2*n,n) + C(3*n,n).at n=6A029848
• Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 98 ones.at n=17A031866
• Last member of a sexy prime quadruple: value of p+18 such that p, p+6, p+12 and p+18 are all prime.at n=34A046124
• Fourth term of balanced prime quartets: p(m-2)-p(m-3) = p(m-1)-p(m-2) = p(m)-p(m-1).at n=14A054803
• Primes with 19 as smallest positive primitive root.at n=17A061331
• Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.at n=29A079451
• Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.at n=38A089528
• Order in which prime factors first occur in the Lucas sequence.at n=30A096362
• Primes of the form Sum_{k=1..n} phi(prime(k)).at n=15A101302
• Smallest prime such that n*k(n)^2+n*k(n)+1 is a prime > (n-1)*k(n-1)^2+(n-1)*k(n-1)+1 with k(n)>1 or 0 if n=4 as no prime possible.at n=23A104995
• Primes with digit sum = 31.at n=27A106767
• Prime differences of tribonacci numbers.at n=19A113239
• Primes p that divide Fibonacci[(p-1)/7].at n=25A125253
• Smallest prime of the form k*prime(n+1)+prime(n) = j*prime(n+2)+prime(n+1) for free integer multipliers k and j.at n=23A129918
• Primes congruent to 30 mod 61.at n=37A142828
• Primes in toothpick sequence A153006.at n=24A153009
• a(n) = 18*a(n-1) - 79*a(n-2) for n>1, a(0)=1, a(1)=13.at n=4A163415
• First of a run of 4 or more consecutive primes which all equal 1 (mod 3).at n=45A185942
• Second-largest prime factor of the n-th Fibonacci number, if composite, or 1 otherwise.at n=55A193615
• Second-smallest prime factor of the n-th Lucas number (beginning with 2), if composite, or 1 otherwise.at n=29A194086