212701

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=38A000230
• Number of protruded partitions of n with largest part at most 3.at n=21A005404
• Primes for which the seven closest primes are smaller.at n=20A075043
• a(n) is the smallest prime p of the form 4k+1 such that nextprime(p) - p = 4n.at n=18A082099
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=29A082890
• The first primes in centuries with three primes.at n=13A157131
• Primes p followed by a gap of at least 1/2 * log(p)^2.at n=17A211073
• 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=11A217724
• a(n) is the smallest prime p such that the gap between p and the next prime is 4*n.at n=18A301925
• Primes preceding the first-occurrence gaps in A014320.at n=39A335366
• 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=38A363544
• 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=38A368640
• Prime numbersat n=19026