63697

Properties

Appears in sequences

• Second term of balanced prime quartets: p(m)-p(m-1) = p(m+1)-p(m) = p(m+2)-p(m+1).at n=22A054801
• The O(1) loop model on the square lattice is defined as follows: At every vertex the loop turns to the left or to the right with equal probability, unless the vertex has been visited before, in which case the loop leaves the vertex via the unused edge. Every vertex is visited twice. The probability that a face of the lattice on an n X infinity cylinder is surrounded by one loop is conjectured to be given by a(n)/A_{HT}(n)^2, where A_{HT}(n) is the number of n X n half turn symmetric alternating sign matrices.at n=5A092373
• Balanced primes (A090403) of index 4.at n=6A096708
• 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, -1, 1), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}.at n=13A148004
• Numbers k such that k and k+6 are both balanced primes.at n=22A173892
• Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..6 array extended with zeros and convolved with 1,1.at n=22A222332
• Number of 6Xn -1,1 arrays such that the sum over i=1..6,j=1..n of i*x(i,j) is zero, the sum of x(i,j) is zero, and rows are nondecreasing (number of ways to distribute n-across galley oarsmen left-right at 6 fore-aft positions so that there are no turning moments on the ship).at n=23A225346
• Number of n X 3 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.at n=7A299888
• T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.at n=47A299893
• T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.at n=52A299893
• Prime numbersat n=6387