21419

Properties

Appears in sequences

• Fourth term of weak prime sextet: p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).at n=6A054831
• Numbers k such that (12^k + 1)/13 is a prime.at n=6A057178
• a(n) = n*(n^2 - 1)/2 - 1.at n=33A117560
• Father primes of order 8.at n=33A136077
• Prime numbers p such that p^3 - (p+1)^2 and p^3 + (p+1)^2 are both primes.at n=22A137476
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 0), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.at n=8A149698
• Primes of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=4.at n=31A152294
• a(1) = 1; thereafter a(n) is always the smallest integer > a(n-1) not leading to a contradiction, such that any five consecutive digits in the sequence sum up to a prime.at n=42A152605
• Primes of the form 3*k^2 + 9*k + 5.at n=31A171838
• In those partitions of n with every part >=3, the total number of parts (counted with multiplicity).at n=44A177739
• Smaller of two consecutive primes whose product of digits is equal and nonzero.at n=7A230083
• Primes p such that 2*p + 11 is a square.at n=29A269784
• Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that abs(j/k - q) is a new minimum.at n=15A355513
• Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that q - j/k is a new minimum, i.e., q is approximated from below.at n=23A355514
• For n >= 1, a(n) is the least prime p such that the arithmetic mean of (n + 1) consecutive primes starting with p is a perfect square, or a(n) = -1 if no such p exists.at n=39A365706
• Prime numbersat n=2405