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A370094 Rectangular array read by antidiagonals: A(n,k) = prime(A114537(n,k)).

%I A370094 #12 Mar 29 2025 03:27:07
%S A370094 2,3,7,5,17,13,11,59,41,19,31,277,179,67,23,127,1787,1063,331,83,29,
%T A370094 709,15299,8527,2221,431,109,37,5381,167449,87803,19577,3001,599,157,
%U A370094 43,52711,2269733,1128889,219613,27457,4397,919,191,47,648391,37139213
%N A370094 Rectangular array read by antidiagonals: A(n,k) = prime(A114537(n,k)).
%C A370094 The rows and columns are all increasing, and every prime occurs exactly once.
%F A370094 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 A370094 Also, removing column 1 of array A114537 leaves the present array.
%e A370094 Corner:
%e A370094    2    3      5     11      31      127       709
%e A370094    7    17    59    277    1787    15299    167449
%e A370094   13    41   179   1063    8527    87803   1128889
%e A370094   19    67   331   2221   19577   219613   3042161
%e A370094   23    83   431   3001   27457   318211   4535189
%e A370094   29   109   599   4397   42043   506683   7474967
%t A370094 NonPrime[n_] := FixedPoint[n + PrimePi@# + 1 &, n];
%t A370094 t[n_, k_] := Nest[Prime, NonPrime[n], k];
%t A370094 Table[Prime[t[n - k, k]], {n, 0, 9}, {k, n, 0, -1}] // Flatten
%t A370094 Table[Prime[t[n, k]], {n, 0, 6}, {k, 0, 10}] // TableForm
%t A370094 (* after _Robert G. Wilson v_ in A114537 *)
%Y A370094 Cf. A000040, A007821, A114537.
%K A370094 nonn,tabl
%O A370094 1,1
%A A370094 _Clark Kimberling_, Feb 09 2024