27061

Properties

Appears in sequences

• Expansion of 1/((1-3x)*(1-5x)*(1-10x)).at n=4A017916
• a(n) = (n-1)*(n-2)^3 - A003878(n-3), with a(1) = a(2) = 0 and a(3) = 2.at n=35A075681
• Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d = 2, 4 or 6) and forming d-pattern = [6, 6, 4]; short d-string notation of pattern = [664].at n=18A078858
• a(n) is the smallest prime == 1 (mod F(n)) where F(n) is the n-th Fibonacci number.at n=19A087384
• Row sums of triangle A091700.at n=7A091701
• Row sums of triangle A135858.at n=30A135859
• Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=9.at n=35A143460
• 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, 1), (-1, 1, 1), (1, -1, -1), (1, 1, 0)}.at n=9A149154
• Primes p0 such that p0+p1+p2-+2 are primes; p0,p1,p2 are three consecutive primes.at n=30A158351
• Chebyshev transform of A107841.at n=6A160852
• Number of binary strings of length n with no substrings equal to 0001, 1000 or 1001.at n=16A164485
• Noncomposite numbers in the southwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.at n=20A168026
• Primes of the form n^2 + n + 1 where n is nonprime.at n=38A185632
• Number of 4X3 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 4 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).at n=8A192704
• Primes p such that p-2 and q are primes, where q is concatenation of binary representations of p and p-2: q = p * 2^L + p-2, where L is the length of binary representation of p-2: L=A070939(p-2).at n=37A232237
• Number of length n binary words such that maximal runs of 1's are restricted to length one or two and maximal runs of 0's are of odd length.at n=21A236340
• Primes p such that q = p^2 - 2, r = q^2 - 2 and s = r^2 - 2 are also prime.at n=7A257552
• Twin prime pairs of the form (k^2 + k - 1, k^2 + k + 1).at n=45A265006
• Primes of the form 1 + n + n^2 + n^3 + ... + n^k, n > 1, k > 1 where n is not prime.at n=38A285017
• Numbers n such that both n-1 and n are nonsquares and the least positive solutions to the Pell equations x1^2 - n*y1^2 =1 and x0^2-(n-1)*y0^2 = 1 have a record for rho(n)=log(x1)/log(x0).at n=22A303604