265621

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=41A000230
• Primes for which the seven closest primes are smaller.at n=27A075043
• Primes for which the eight closest primes are smaller.at n=7A075050
• Smallest prime for which the n closest primes are smaller.at n=9A075051
• Smallest prime p such that there is a gap of exactly 2*prime(n) between p and the next prime.at n=12A080082
• 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=12A081413
• Middle q of three consecutive primes p,q,r, such that one adjacent prime is near, the other is far and the ratio of the differences (whichever of (r-q)/(q-p) or (q-p)/(r-q) is greater than 1) sets a record.at n=17A084105
• Primes p followed by a gap of at least 1/2 * log(p)^2.at n=18A211073
• Smallest prime producing a gap with the next prime, the size of the gap being a composite number with 2n+1 as a factor.at n=12A217724
• Primes of the form 2*n^2+30*n+13.at n=29A243889
• Positive solutions of Monkey and Coconuts Problem for the classic case (5 sailors, 1 coconut to the monkey): a(n) = 15625*n - 4 for n >= 1.at n=16A254029
• a(n) is the least prime p such that the second forward difference of three consecutive primes p, q and r is n = -(p - 2q + r)/2.at n=38A316792
• Primes preceding the first-occurrence gaps in A014320.at n=40A335366
• a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime, but prime(n+1) does not divide any of these.at n=35A341640
• a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime.at n=34A341650
• a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime.at n=35A341650
• Primes p such that the squarefree kernel of the product of the composite numbers between p and the next prime after p (A076978) sets a new record.at n=38A354217
• Least prime p such that 2n can be written as the sum or absolute difference of p and the next prime, or -1 if no such prime exists.at n=41A363544
• a(0) = 2; for n > 0, a(n) is the smallest prime that differs from the next prime by 2n and is not part of a run of 3 or more consecutive primes in arithmetic progression, or -1 if no such prime exists.at n=41A368640
• a(n) = smallest prime Q of a consecutive prime triple {P, Q, R} such that floor( (R-Q) * (Q-P) / 8 ) = n.at n=19A375009