51109

Properties

Appears in sequences

• 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=43A036006
• a(n) = p is the smallest prime such that p = n + h(n)^2 and p is the first prime following h(n)^2. The smallest immediate post-square primes with distance n = p - h(n)^2.at n=32A058056
• Least positive integer multiples of angle x such that their direction cosines form a unit vector: Sum_{k>0} cos(a(k)*x)^2 = 1, where a(1)=1 and x=1.at n=18A080136
• Primes p such that p-2 and p+2 are divisible by a cube.at n=6A089202
• 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, 1), (-1, 0, 1), (0, 1, -1), (1, 0, 0)}.at n=12A148079
• Prime numbers with gaps larger than 18 towards both neighboring primes.at n=37A163111
• Prime numbers with gaps larger than 20 towards both neighboring primes.at n=18A163112
• Primes obtained from other primes by prefixing a 5.at n=40A165555
• Number of 2 X 2 nonsingular 0..n matrices with a(1,1) <= a(1,2) <= a(2,1) <= a(2,2).at n=30A183763
• Primes p=u^2+v^2 such that p+u or p+v is the next prime after p.at n=37A213996
• Primes of a056240-type 3.at n=37A300359
• Primes P where the distance to the nearest prime is greater than 2*log(P).at n=33A330426
• Index where n first appears in A381597.at n=48A381599
• Positive numbers k such that (sin k)^k sets a new record.at n=11A383540
• Prime numbersat n=5230