OFFSET
1,2
COMMENTS
The sequence is a permutation of the natural numbers.
Theorem: Let v(y) denote the 2-adic valuation of y. For x an odd natural number, let F(x) = (3*x+1)/2^v(3*x+1) (see A075677). Row n of A is the set of all natural numbers m such that v(1+F(4*(2*m-1)-3)) = n.
FORMULA
A(n,k) = (1 + A257499(n,k))/2.
EXAMPLE
Array begins:
. 1 3 5 7 9 11 13 15 17 19
. 4 8 12 16 20 24 28 32 36 40
. 2 10 18 26 34 42 50 58 66 74
. 14 30 46 62 78 94 110 126 142 158
. 6 38 70 102 134 166 198 230 262 294
. 54 118 182 246 310 374 438 502 566 630
. 22 150 278 406 534 662 790 918 1046 1174
. 214 470 726 982 1238 1494 1750 2006 2262 2518
. 86 598 1110 1622 2134 2646 3158 3670 4182 4694
. 854 1878 2902 3926 4950 5974 6998 8022 9046 10070
MATHEMATICA
(* Array: *)
Grid[Table[(2 + 2^(n - 1)*(6*k - 3 + 2*(-1)^n))/3, {n, 10}, {k, 10}]]
(* Array antidiagonals flattened: *)
Flatten[Table[(2 + 2^(n - k)*(6*k - 3 + 2*(-1)^(n - k + 1)))/3, {n, 10}, {k, n}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, May 29 2015
STATUS
approved