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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.
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
1,1
COMMENTS
Every primes appears exactly once in the array.
FORMULA
A(n,k) = A000040(A054582(n-1,k-1)).
A(A001511(m),A003602(m)) = A000040(m), m >= 1.
EXAMPLE
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
...
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}]]
CROSSREFS
Cf. A031368, A031378, A031395 (rows 1--3).
Cf. A033844 (column 1).
Cf. A264735 (main diagonal).
Sequence in context: A185956 A316885 A225039 * A262350 A228891 A168484
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Nov 22 2015
STATUS
approved