|
%I #12 Dec 03 2015 04:22:49
%S 2,3,5,7,13,11,19,37,29,17,53,89,71,43,23,131,223,173,107,61,31,311,
%T 503,409,263,151,79,41,719,1163,941,613,359,193,101,47,1619,2657,2129,
%U 1423,827,457,239,113,59,3671,5849,4751,3167,1877,1049,569,281,139,67
%N 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.
%C Every primes appears exactly once in the array.
%F A(n,k) = A000040(A054582(n-1,k-1)).
%F A(A001511(m),A003602(m)) = A000040(m), m >= 1.
%e The array begins:
%e . 2 5 11 17 23 31 41 47 59 67
%e . 3 13 29 43 61 79 101 113 139 163
%e . 7 37 71 107 151 193 239 281 337 383
%e . 19 89 173 263 359 457 569 659 769 881
%e . 53 223 409 613 827 1049 1283 1511 1747 2003
%e . 131 503 941 1423 1877 2377 2861 3413 3923 4481
%e . 311 1163 2129 3167 4211 5309 6379 7561 8731 9857
%e . 719 2657 4751 6971 9311 11731 14143 16603 19183 21661
%e . 1619 5849 10459 15331 20393 25579 30859 36161 41611 47143
%e . 3671 12907 22943 33479 44269 55487 66791 78193 89899 101573
%e As a triangle:
%e . 2
%e . 3 5
%e . 7 13 11
%e . 19 37 29 17
%e . 53 89 71 43 23
%e . 131 223 173 107 61 31
%e . 311 503 409 263 151 79 41
%e ...
%t (* Array: *)
%t Grid[Table[Prime[2^(n - 1)*(2*k - 1)], {n, 10}, {k, 10}]]
%t (* Array antidiagonals flattened: *)
%t Flatten[Table[Prime[2^(n - k)*(2*k - 1)], {n, 10}, {k, n}]]
%Y Cf. A031368, A031378, A031395 (rows 1--3).
%Y Cf. A033844 (column 1).
%Y Cf. A264735 (main diagonal).
%Y Cf. A000040, A001511, A003602, A054582.
%K nonn,tabl
%O 1,1
%A _L. Edson Jeffery_, Nov 22 2015
|
