This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A083050 Square table read by antidiagonals forms a permutation of the natural numbers: T(n,0) = floor(n*x/(x-1))+1, T(n,k+1) = ceiling(x*T(n,k)), where x = sqrt(2), n>=0, k>=0. 15
 1, 2, 4, 3, 6, 7, 5, 9, 10, 11, 8, 13, 15, 16, 14, 12, 19, 22, 23, 20, 18, 17, 27, 32, 33, 29, 26, 21, 25, 39, 46, 47, 42, 37, 30, 24, 36, 56, 66, 67, 60, 53, 43, 34, 28, 51, 80, 94, 95, 85, 75, 61, 49, 40, 31, 73, 114, 133, 135, 121, 107, 87, 70, 57, 44, 35, 104, 162, 189 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First column is A083051, main diagonal is A083052, antidiagonal sums give A083053. A083050 is the dispersion of the sequence given by floor(1+n*sqrt(2)); for a discussion of dispersions, see A191429. LINKS EXAMPLE Table begins:    1  2  3   5   8  12  17  25  36  51   73  104 ...    4  6  9  13  19  27  39  56  80 114  162  230 ...    7 10 15  22  32  46  66  94 133 189  268  380 ...   11 16 23  33  47  67  95 135 191 271  384  544 ...   14 20 29  42  60  85 121 172 244 346  490  693 ...   18 26 37  53  75 107 152 215 305 432  611  865 ...   21 30 43  61  87 124 176 249 353 500  708 1002 ...   24 34 49  70  99 141 200 283 401 568  804 1138 ...   28 40 57  81 115 163 231 327 463 655  927 1311 ...   31 44 63  90 128 182 258 365 517 732 1036 1466 ...   35 50 71 101 143 203 288 408 577 817 1156 1635 ... MATHEMATICA (* program generates the dispersion array T of the complement of increasing sequence f[n] *) r = 40; r1 = 12; (* r=# rows of T, r1=# rows to show *) c = 40; c1 = 12; (* c=# cols of T, c1=# cols to show *) x = Sqrt[2]; f[n_] := Floor[n*x + 1] (* f(n) is complement of column 1 *) mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]] rows = {NestList[f, 1, c]}; Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}]; t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A083050 as an array *) Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* array as a sequence *) (* Program by Peter J. C. Moses, Jun 01 2011, added here Jun 03 2011 by Clark Kimberling *) CROSSREFS Cf. A083051, A083052, A083053, A083044, A083047, A191429. Sequence in context: A216623 A297551 A297673 * A194030 A083044 A126714 Adjacent sequences:  A083047 A083048 A083049 * A083051 A083052 A083053 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Apr 18 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 17:32 EST 2019. Contains 329979 sequences. (Running on oeis4.)