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%I #8 Feb 16 2024 15:08:50
%S 2,3,7,5,17,13,11,59,41,19,31,277,179,67,23,127,1787,1063,331,83,29,
%T 709,15299,8527,2221,431,109,37,5381,167449,87803,19577,3001,599,157,
%U 43,52711,2269733,1128889,219613,27457,4397,919,191,47,648391,37139213
%N Rectangular array read by antidiagonals: A(n,k) = prime(A114537(n,k)).
%C The rows and columns are all increasing, and every prime occurs exactly once.
%F Let f(n) = A007821(n) and p(n) = prime(n). Row n of the array begins with f(n), followed by p(f(n), p(p(f(n))), p(p(p(f(n)))), ...
%F Also, removing column 1 of array A114537 leaves the present array.
%e Corner:
%e 2 3 5 11 31 127 709
%e 7 17 59 277 1787 15299 167449
%e 13 41 179 1063 8527 87803 1128889
%e 19 67 331 2221 19577 219613 3042161
%e 23 83 431 3001 27457 318211 4535189
%e 29 109 599 4397 42043 506683 7474967
%t NonPrime[n_] := FixedPoint[n + PrimePi@# + 1 &, n];
%t t[n_, k_] := Nest[Prime, NonPrime[n], k];
%t Table[Prime[t[n - k, k]], {n, 0, 9}, {k, n, 0, -1}] // Flatten
%t Table[Prime[t[n, k]], {n, 0, 6}, {k, 0, 10}] // TableForm
%t (* after _Robert G. Wilson v_ in A114537 *)
%Y Cf. A000040, A007821, A114537.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Feb 09 2024