415069

Properties

Appears in sequences

• Largest k such that round(1/(sqrt(prime(k+1))-sqrt(prime(k)))) = n where prime(n) denotes the n-th prime (conjectured values).at n=33A078693
• Numbers where A080374 increases.at n=28A080376
• Values of k 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=25A084976
• First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.at n=34A103669
• Primes with distinct digits appearing in partition of decimal expansion of Pi.at n=37A104820
• Greatest k for which the Andrica-like conjectural inequalities, prime(k+1)-prime(k)-(1/n)*sqrt(prime(k)) < 0, appear to fail, based on empirical evidence.at n=16A161623
• Greatest k for which the Andrica-like conjectural inequalities, prime(k+1)-prime(k)-(1/n)*sqrt(prime(k)) < 0, appear to fail, based on empirical evidence.at n=17A161623
• a(n) is the least k such that the number of integers between (1/5)*prime(k) and (1/5)*prime(k+1) is n.at n=28A390786
• Prime numbersat n=35006