34061

Properties

Appears in sequences

• a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.at n=31A000230
• Primes of the form j^2 + (j+1)^2.at n=42A027862
• a(n) = Min{ q prime | nextprime(q) - q - 1 = prime(n)}, or 0 if none exist.at n=16A063793
• Primes p such that the p-1 digits of the decimal expansion of k/p (for k=1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.at n=3A072359
• Primes for which the five closest primes are smaller.at n=22A075037
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=5A079098
• Smallest prime p such that there is a gap of exactly 2*prime(n) between p and the next prime.at n=10A080082
• a(n) is the smallest prime p such that the largest prime divisor of the difference nextprime(p) - p equals the n-th prime, prime(n).at n=10A081413
• Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.at n=10A082889
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=3A082890
• Primes that show the slow decrease in the larger values of the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime.at n=11A084974
• Primes of the form (4*k + 3)^2 + (4*k + 2)^2 where k=0,1,2,3,...at n=13A087872
• Primes of the form 8*n^2 + 4*n + 1.at n=22A102130
• Numbers appearing in A122072 at least four times.at n=21A122390
• Primes p such that log(nextPrime(p))/log(p) is smaller for larger primes.at n=41A144104
• Primes of the form prime(x)^2 + (prime(x) - 1)^2.at n=13A147718
• Primes of the form 50n^2 + 10n + 1.at n=13A154428
• a(n) is the smallest prime q such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator n (or 0, if such a prime does not exist).at n=30A168253
• Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).at n=17A193393
• Number of partitions of 5n such that cn(0,5) <= cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5).at n=15A202087