40933

Properties

Appears in sequences

• Indices of primes where largest gap occurs.at n=17A005669
• 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=11A078693
• 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=17A084976
• Indices of primes where nondecreasing gaps occur.at n=33A085500
• First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.at n=29A103669
• Triangular array read by rows: T(n,1) = T(n,n) = 1, T(n,k) = 3*T(n-1,k-1) + 2*T(n-1,k).at n=48A119725
• 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=6A161623
• Number of (w,x,y,z) with all terms in {1,...,n} and w >= harmonic mean of {x,y,z}.at n=16A212107
• Least number x such that there are n numbers of the form 6k-1 or 6k+1 between prime(x) and prime(x+1).at n=37A213903
• Indices of the primes in A073861 (n-digit primes followed by a maximal gap).at n=5A241623
• Satisfies Sum_{n>=0} a(n)*x^n = x / Product_{n>=0} (1 - x^n/(1 - x^n))^a(n).at n=12A248870
• Number of broken 3-diamond partitions of n.at n=17A328541
• a(n) is the index k of prime(k), such that abs(prime(k) - Sum_{j=k-2..k+2} prime(j)/5) sets a new record.at n=22A337438
• a(n) is the index k of prime(k), such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)/3) sets a new record.at n=15A337488
• Primes p such that if q is the next prime, p+A004086(q) and q+A004086(p) are prime.at n=44A351728
• 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=22A390786
• a(n) is the least k such that there are exactly n integers between (1/6)*prime(k) and (1/6)*prime(k+1).at n=18A390787
• Prime numbersat n=4286