A283738 Array read by antidiagonals: row k shows the numbers m such that 1/(k+1) < f(m) < 1/k, where f(m) = fractional part of m*(golden ratio).

1, 3, 4, 6, 12, 7, 8, 20, 15, 2, 9, 25, 28, 23, 10, 11, 33, 49, 36, 44, 31, 14, 38, 62, 57, 65, 86, 52, 16, 41, 70, 78, 99, 120, 107, 18, 17, 46, 83, 91, 133, 175, 141, 73, 39, 19, 54, 96, 112, 154, 230, 196, 162, 128, 94, 21, 59, 104, 146, 188, 264, 251

Offset

1,2

Comments

A permutation of the positive integers.

The difference between any two consecutive terms in any row is a Fibonacci number, as is the difference between any two consecutive terms in column 1.

Links

Table of n, a(n) for n=1..62.

Formula

Northwest corner:

1 3 6 8 9 11 14 16 17

4 12 20 25 33 38 41 46 54

7 15 28 49 62 70 83 96 104

2 23 36 57 78 91 112 146 167

10 44 65 99 133 154 188 209 243

31 86 120 175 230 264 319 353 374

Mathematica

g = GoldenRatio; z = 5000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], 1/(k + 1) < t[[#]] < 1/k &];
s[n_] := Take[r[n], Min[20, Length[r[n]]]];
TableForm[Table[s[k], {k, 1, 14}]] (* A283738, array *)
w[i_, j_] := s[i][[j]]; Flatten[Table[w[n - k + 1, k], {n, 14}, {k, n, 1, -1}]]  (* A283738, sequence *)

Crossrefs

Cf. A000045, A001622, A283739, A283740, A283741, A283745.

Sequence in context: A048229 A002090 A199970 * A366535 A368469 A366439

Adjacent sequences: A283735 A283736 A283737 * A283739 A283740 A283741

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Mar 16 2017

Status

approved