A264731 Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = prime(2^(n-1)*(2*k-1)), n,k >= 1.

2, 3, 5, 7, 13, 11, 19, 37, 29, 17, 53, 89, 71, 43, 23, 131, 223, 173, 107, 61, 31, 311, 503, 409, 263, 151, 79, 41, 719, 1163, 941, 613, 359, 193, 101, 47, 1619, 2657, 2129, 1423, 827, 457, 239, 113, 59, 3671, 5849, 4751, 3167, 1877, 1049, 569, 281, 139, 67

Offset: 1

Author

L. Edson Jeffery, Nov 22 2015

Keywords

• nonn
• tabl

Comments

Every primes appears exactly once in the array.

Examples

			The array begins:
.     2      5     11     17     23     31     41     47     59      67
.     3     13     29     43     61     79    101    113    139     163
.     7     37     71    107    151    193    239    281    337     383
.    19     89    173    263    359    457    569    659    769     881
.    53    223    409    613    827   1049   1283   1511   1747    2003
.   131    503    941   1423   1877   2377   2861   3413   3923    4481
.   311   1163   2129   3167   4211   5309   6379   7561   8731    9857
.   719   2657   4751   6971   9311  11731  14143  16603  19183   21661
.  1619   5849  10459  15331  20393  25579  30859  36161  41611   47143
.  3671  12907  22943  33479  44269  55487  66791  78193  89899  101573
As a triangle:
.    2
.    3    5
.    7   13   11
.   19   37   29   17
.   53   89   71   43   23
.  131  223  173  107   61  31
.  311  503  409  263  151  79  41
...
		

Crossrefs

Cf. A031368, A031378, A031395 (rows 1--3).

Cf. A033844 (column 1).

Cf. A264735 (main diagonal).

Cf. A000040, A001511, A003602, A054582.

Programs

Mathematica

(* Array: *)
Grid[Table[Prime[2^(n - 1)*(2*k - 1)], {n, 10}, {k, 10}]]
(* Array antidiagonals flattened: *)
Flatten[Table[Prime[2^(n - k)*(2*k - 1)], {n, 10}, {k, n}]]

Formula

A(n,k) = A000040(A054582(n-1,k-1)).

A(A001511(m),A003602(m)) = A000040(m), m >= 1.