31545

Appears in sequences

• Indices of primes where largest gap occurs.at n=16A005669
• Generalized Lucas numbers.at n=16A006491
• Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly four ways.at n=8A076457
• 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=10A078693
• 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=16A084976
• Indices of primes where nondecreasing gaps occur.at n=32A085500
• Where the records (A098968) occur in A046930 (if initial term is 0 not 1).at n=24A098969
• First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.at n=32A103669
• 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=5A161623
• 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=36A213903
• Index of the primes of A205827, A000720(A205827(n)).at n=11A214935
• Least number k for which primepi(prime(k+1)/2) - primepi(prime(k)/2) = n.at n=8A215237
• Indices of record values in A228098.at n=11A230777
• Indices (i.e., value of A000720 = primepi) of primes in A111870.at n=10A241542
• Row 5 of A277710: Positions of 5's in A264977; positions of 10's in A277330.at n=49A277715
• G.f.: 1 + Sum_{n=-oo..+oo, n<>0} (x - x^n)^n / (1 - (x - x^n)^n).at n=22A294677
• Number of nX5 0..1 arrays with every element unequal to 0, 1, 2, 6, 7 or 8 king-move adjacent elements, with upper left element zero.at n=9A316690
• 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=21A337438
• 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=14A337488
• a(n) is the least k such that there are exactly n primes between prime(k) + 1 and floor(prime(k + 1)^2/prime(k)) (inclusive) or 0 if no such k exists.at n=13A344582