19609

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=26A000230
• Primes (lower end) with record gaps to the next consecutive prime: primes p(k) where p(k+1) - p(k) exceeds p(j+1) - p(j) for all j < k.at n=12A002386
• Increasing gaps between prime-powers.at n=17A002540
• Number of Twopins positions.at n=50A005686
• Primes that are palindromic in base 2 (but written here in base 10).at n=34A016041
• Lower prime of a record difference between it and the second prime after it.at n=16A031133
• Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 93.at n=0A031681
• Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.at n=28A046931
• Row 5 of square array defined in A047671.at n=8A047674
• Array A read by diagonals; n-th difference of (A(k,n), A(k,n-1),..., A(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...at n=59A047848
• a(n) = A047848(4, n).at n=6A047852
• Numbers k such that 5^k - 4^k is prime.at n=12A059802
• Primes for which the five closest primes are smaller.at n=8A075037
• Primes for which the six closest primes are smaller.at n=3A075038
• a(n) is the smallest prime p of the form 4k+1 such that nextprime(p) - p = 4n.at n=12A082099
• Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.at n=4A082889
• Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.at n=0A082890
• Smallest prime p such that q = (r-p)/log(p) > n, where r is the next prime after p.at n=4A082891
• Primes of the form x^5 + x^4 + x^3 + x^2 + x + 2.at n=3A088549
• Primes p such that the sum of the digits of p is not prime, but the sum of each digit raised to the 4th power is prime.at n=13A091368