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A377173 Rectangular array, by antidiagonals: (row 1) = r(1) = A000040 (primes); (row n) = r(n) = prime(r(n-1)) for n>=1.

%I A377173 #4 Oct 19 2024 18:09:20
%S A377173 2,3,3,5,5,5,7,11,11,11,11,17,31,31,31,13,31,59,127,127,127,17,41,127,
%T A377173 277,709,709,709,19,59,179,709,1787,5381,5381,5381,23,67,277,1063,
%U A377173 5381,15299,52711,52711,52711
%N A377173 Rectangular array, by antidiagonals: (row 1) = r(1) = A000040 (primes); (row n) = r(n) = prime(r(n-1)) for n>=1.
%F A377173 A049076(n) = number of appearances of prime(n).
%e A377173 corner:
%e A377173    2     3      5       7      11       13       17
%e A377173    3     5     11      17      31       41       59
%e A377173    5    11     31      59     127      179      277
%e A377173   11    31    127     277     709     1063     1787
%e A377173   31   127    709    1787    5381     8527    15299
%e A377173  127   709   5381   15299   52711    87803   167449
%e A377173  709  5381  52711  167449  648391  1128889  2269733
%t A377173 r[0] = Range[16];
%t A377173 r[n_] := r[n] = Prime[r[n - 1]]
%t A377173 Grid[Table[r[n], {n, 1, 6}]]  (* array *)
%t A377173 p[n_, k_] := r[n][[k]];
%t A377173 Table[p[n - k + 1, k], {n, 9}, {k, n, 1, -1}] // Flatten  (* sequence *)
%Y A377173 Cf. A000040 (row 1), A007097 (column 1), A006450 (row 2), A038580 (row 3), A058009 (principal diagonal), A049076, A114537, A377181.
%K A377173 nonn,tabl
%O A377173 1,1
%A A377173 _Clark Kimberling_, Oct 19 2024