43331

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=30A000230
• Primes that are palindromic in base 14.at n=34A029981
• Number of partitions of n into parts not of the form 25k, 25k+7 or 25k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 11 are greater than 1.at n=42A036006
• Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.at n=34A046931
• Write fundamental unit for real quadratic field of discriminant n as x + y*omega; sequence gives values of x for n == 1 mod 4.at n=40A053370
• Smallest prime p such that there is a gap of 6n between p and the next prime.at n=9A058193
• a(n) = Min{ q prime | nextprime(q) - q - 1 = prime(n)}, or 0 if none exist.at n=15A063793
• Product_{i=1..3} (i+x) / Product_{i=1..3} (i-x) = Sum_{n>=0} (a(n)/b(n))*x^n.at n=5A068179
• Primes for which the five closest primes are smaller.at n=30A075037
• Conjectured values of greatest k such that for any consecutive primes q, q', k <= q < q', sqrt(q')-sqrt(q) < 1/n.at n=6A079098
• Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime terms of A074776.at n=18A080050
• a(n) is the smallest prime p of the form 4k+3 such that nextprime(p) - p = 4n.at n=14A082098
• Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.at n=18A082889
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=7A082890
• Primes prime(j) such that prime(j)-j is a true power of prime.at n=15A083240
• Primes 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=12A084974
• Primes arising in A073946.at n=17A113943
• Numbers appearing in A122072 at least four times.at n=37A122390
• Primes p such that q-p = 60, where q is the next prime after p.at n=0A126771
• Prime numbers p of the form 10k+1 for which the quintic polynomial x^5-x-1 modulus p is factorizable into five binomials.at n=10A135842