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%I #6 Oct 19 2024 22:13:40
%S 4,6,9,8,12,16,9,15,21,26,10,16,25,33,39,12,18,26,38,49,56,14,21,28,
%T 39,55,69,78,15,24,33,42,56,77,94,106,16,25,36,49,60,78,105,125,141,
%U 18,26,38,52,69,84,106,140,164,184,20,28,39,55,74,94,115,141,183,212,236
%N Rectangular array, by antidiagonals: (row 1) = r(1) = A002808 (composite numbers); (row n) = r(n) = A002808(r(n-1)) for n>=1.
%F A059981(n) = number of appearances of A002808(n).
%e corner:
%e 4 6 8 9 10 12 14 15 16 18
%e 9 12 15 16 18 21 24 25 26 28
%e 16 21 25 26 28 33 36 38 39 42
%e 26 33 38 39 42 49 52 55 56 60
%e 39 49 55 56 60 69 74 77 78 84
%e 56 69 77 78 84 94 100 105 106 115
%e 78 94 105 106 115 125 133 140 141 152
%t c[n_] := c[n] = Select[Range[500], CompositeQ][[n]]
%t r[0] = Table[c[n], {n, 1, 10}]
%t r[n_] := r[n] = c[r[n - 1]]
%t Grid[Table[r[n], {n, 0, 6}]] (* array *)
%t p[n_, k_] := r[n][[k]];
%t Table[p[n - k + 1, k], {n, 0, 9}, {k, n + 1, 1, -1}] // Flatten (* sequence *)
%Y Cf. A002808 (row 1), A050545 (row 2), A280327 (row 3), A006508 (column 1), A022450 (column 2), A023451 (column 3), A059981, A236356, A280327 (principal diagonal), A377173, A114577 (dispersion of the composite numbers).
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Oct 19 2024