19421

Properties

Appears in sequences

• Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime.at n=18A007530
• Numbers k such that the continued fraction for sqrt(k) has period 75.at n=16A020414
• Initial members p of prime 5-tuples (p, p+2, p+6, p+8, p+12).at n=5A022006
• a(n) = [ (n-2)nd elementary symmetric function of {log(k)} ], k = 2,3,...,n.at n=12A025208
• Number of rooted compound windmills (mobiles) of n nodes with no symmetries.at n=13A032171
• Initial terms of '4-block' primes as described in A032591.at n=29A032592
• Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 23.at n=28A051964
• Let f(m) = smallest prime that divides k^2 + k + m for k = 0,1,2,...; sequence gives smallest m >= 2 such that f(m) is the n-th prime, or -1 if no such m exists.at n=14A060380
• Let f(m) = smallest prime that divides k^2 + k + m for k = 0,1,2,...; sequence gives smallest m >= 0 such that f(m) is the n-th prime.at n=14A060392
• Suppose p and q = p+20 are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are 56 possible difference patterns, shown in the Comments line. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.at n=55A079020
• Primes p such that three (the maximum number) primes occur between p and p+12.at n=13A086140
• Primes congruent to 23 mod 53.at n=39A142553
• Primes congruent to 10 mod 59.at n=36A142737
• Primes congruent to 23 mod 61.at n=36A142821
• Initial members of prime triples (p, p+2, p+6) for which also the sum 3p+8 is prime.at n=24A162001
• The lesser of twin primes p such that p*q+a+b+c are also the lesser of twin primes, (p and q are twin primes, p+2=q, a=p-1,b=(p+q)/2,c=q+1).at n=20A168536
• Primes p such that (p, p+2, p+6, p+12) is a prime quadruple.at n=30A172454
• The smaller member of a twin prime pair in which both primes are emirps.at n=36A175215
• Chen primes A109611(k) which have the same sum-of-digits as their index k.at n=36A176012
• Larger of emirp pairs whose digital sums are also emirps (A178091).at n=34A178093