A393609 Square array A read by descending antidiagonals: A(n,k) = prime(A035513(n, k)).

2, 3, 7, 5, 17, 13, 11, 31, 29, 23, 19, 61, 53, 47, 37, 41, 109, 101, 89, 71, 43, 73, 211, 181, 167, 131, 83, 59, 139, 383, 337, 307, 239, 157, 107, 67, 257, 677, 601, 557, 433, 281, 197, 127, 79, 461, 1217, 1061, 977, 769, 509, 367, 229, 151, 97, 827, 2137

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..57.

Formula

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

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

Example

Corner:
     2     3     5    11    19    41    73   139   257   461
     7    17    31    61   109   211   383   677  1217  2137
    13    29    53   101   181   337   601  1061  1877  3313
    23    47    89   167   307   557   977  1709  3011  5273
    37    71   131   239   433   769  1373  2393  4211  7309
    43    83   157   281   509   919  1609  2833  4969  8641
    59   107   197   367   647  1153  2039  3571  6217 10733
    67   127   229   419   739  1301  2309  4019  6983 12143
    79   151   271   491   881  1559  2729  4789  8297 14389
    97   179   317   587  1031  1811  3203  5557  9613 16573

Mathematica

f[n_] := Fibonacci[n]; r = GoldenRatio;
w[n_, k_] := f[k + 1]*Floor[n*r] + (n - 1) f[k];
p[n_, k_] := Prime[w[n, k]];
Table[p[n, k], {n, 1, 12}, {k, 1, 12}] // Column
Flatten[Table[p[n, k], {n, 1, 12}, {k, 1, 12}]]  (* array *)
Flatten[Table[p[n - k + 1, k], {n, 1, 12}, {k, n, 1, -1}]]  (* sequence *)

Crossrefs

Cf. A000040, A035513.

Sequence in context: A124440 A067363 A083188 * A370094 A228775 A129543

Adjacent sequences: A393606 A393607 A393608 * A393610 A393611 A393612

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 24 2026

Status

approved