This site is supported by donations to The OEIS Foundation.

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A182801 Joint-rank array of the numbers j*r^(i-1), where r = golden ratio = (1+sqrt(5))/2, i>=1, j>=1, read by antidiagonals. 21
 1, 3, 2, 5, 6, 4, 7, 9, 11, 8, 10, 13, 16, 19, 14, 12, 18, 23, 28, 32, 25, 15, 21, 31, 39, 48, 54, 42, 17, 26, 36, 52, 66, 81, 89, 71, 20, 29, 44, 61, 86, 110, 134, 147, 117, 22, 34, 49, 73, 102, 141, 181, 221, 240, 193, 24, 38, 57, 82 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Joint-rank arrays are introduced here as follows. Suppose that R={f(i,j)} is set of positive numbers, where i and j range through countable sets I and J, respectively, such that for every n, then number f(i,j) < n is finite.  Let T(i,j) be the position of f(i,j) in the joint ranking of all the numbers in R.  The joint-rank array of R is the array T whose i-th row is T(i,j). For A182801, f(i,j)=j*r^(i-1), where r=(1+sqrt(5))/2 and I=J={1,2,3,...}. (row 1)=A020959; (row 2)=A020960; (row 3)=A020961. (col 1)=A020956; (col 2)=A020957; (col 3)=A020958. Every positive integer occurs exactly once in A182801, so that as a sequence it is a permutation of the positive integers. REFERENCES Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176.  Solution published in Vol. 12, No. 1, Winter 2000, pp. 61-62. LINKS FORMULA T(i,j)=Sum{floor(j*r^(i-k)): k>=1}. EXAMPLE Northwest corner: 1....3....5....7...10...12... 2....6....9...13...18...21... 4...11...16...23...31...36... 8...19...28...39...52...61... MATHEMATICA r=GoldenRatio; f[i_, j_]:=Sum[Floor[j*r^(i-k)], {k, 1, i+Log[r, j]}]; TableForm[Table[f[i, j], {i, 1, 16}, {j, 1, 16}]] (* A182801 *) CROSSREFS Cf. A182802, A182846-A182849, A252229. Sequence in context: A227192 A099889 A115511 * A026098 A135764 A253551 Adjacent sequences:  A182798 A182799 A182800 * A182802 A182803 A182804 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 04 2010 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.