A393609 - OEIS

%I #12 Mar 08 2026 18:43:26

%S 2,3,7,5,17,13,11,31,29,23,19,61,53,47,37,41,109,101,89,71,43,73,211,

%T 181,167,131,83,59,139,383,337,307,239,157,107,67,257,677,601,557,433,

%U 281,197,127,79,461,1217,1061,977,769,509,367,229,151,97,827,2137

%N Square array A read by descending antidiagonals: A(n,k) = prime(A035513(n, k)).

%C Every prime occurs exactly once. Every row and every column is strictly increasing.

%F A(n,k) = A000040(A035513(n, k)).

%F a(n) = A000040(A035513(n)).

%e Corner:

%e      2     3     5    11    19    41    73   139   257   461

%e      7    17    31    61   109   211   383   677  1217  2137

%e     13    29    53   101   181   337   601  1061  1877  3313

%e     23    47    89   167   307   557   977  1709  3011  5273

%e     37    71   131   239   433   769  1373  2393  4211  7309

%e     43    83   157   281   509   919  1609  2833  4969  8641

%e     59   107   197   367   647  1153  2039  3571  6217 10733

%e     67   127   229   419   739  1301  2309  4019  6983 12143

%e     79   151   271   491   881  1559  2729  4789  8297 14389

%e     97   179   317   587  1031  1811  3203  5557  9613 16573

%t f[n_] := Fibonacci[n]; r = GoldenRatio;

%t w[n_, k_] := f[k + 1]*Floor[n*r] + (n - 1) f[k];

%t p[n_, k_] := Prime[w[n, k]];

%t Table[p[n, k], {n, 1, 12}, {k, 1, 12}] // Column

%t Flatten[Table[p[n, k], {n, 1, 12}, {k, 1, 12}]]  (* array *)

%t Flatten[Table[p[n - k + 1, k], {n, 1, 12}, {k, n, 1, -1}]]  (* sequence *)

%Y Cf. A000040, A035513.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Feb 24 2026