A182849 Joint-rank array of the numbers j*(i-1+r), where r = golden ratio = (1+sqrt(5))/2, and i>=1, j>=1, by antidiagonals.

1, 3, 2, 6, 7, 4, 9, 13, 11, 5, 14, 19, 21, 16, 8, 18, 27, 31, 30, 22, 10, 23, 36, 43, 45, 39, 28, 12, 26, 44, 56, 61, 57, 50, 34, 15, 32, 52, 68, 78, 79, 73, 60, 40, 17, 37, 63, 83, 94, 101, 98, 87, 70, 47, 20, 42, 72, 96, 113, 124, 126, 118, 104, 82, 54, 24, 48

Offset: 1

Author

Clark Kimberling, Dec 08 2010

Keywords

• nonn
• tabl

Comments

Joint-rank arrays are defined in the first comment at A182801. Every positive integer occurs exactly once, so that as a sequence, A182849 is a permutation of the positive integers.

Examples

			Northwest corner:
1....3....6....9...
2....7...13...19...
4...11...21...31...
5...16...30...45...
		

Crossrefs

Cf. A182801, A182846.

Programs

Mathematica

r=GoldenRatio;
f[i_,j_]:=Sum[Floor[j*(i-1+r)/(k-1+r)],{k,1,1+r+j(i-1+r)}];
TableForm[Table[f[i,j],{i,1,10},{j,1,10}]] (* A182849 *)

Formula

T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=(1+sqrt(5))/2, k>=1} for i>=1, j>=1.