162143

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=33A000230
• a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 3, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1) with a(1) = a(2) = 1.at n=17A049940
• First n-digit prime to begin a gap.at n=5A053299
• Smallest prime p such that there is a gap of 6n between p and the next prime.at n=10A058193
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=22A082890
• Increasing peaks in the prime gap sequence A000230.at n=6A086977
• prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 15.at n=7A109569
• Records in A000230.at n=17A133429
• a(n) is the smallest n-isolated prime, or a(n)=0 if there are no n-isolated primes.at n=37A218275
• Primes p such that q - p = 66, where q is the next prime after p.at n=0A225811
• Least prime such that between it and the next prime there are exactly n semiprimes.at n=22A228171
• Number of (n+1)X(2+1) 0..1 arrays with no 2X2 subblock having zero or two 1s.at n=8A251213
• Primes preceding the first-occurrence gaps in A014320.at n=36A335366
• 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=33A363544
• 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=33A368640
• Prime numbersat n=14862