A283739 Array read by antidiagonals: row k lists the numbers m such that (k-1)/k < f(m) < k/(k+1), where f(m) = fractional part of m*(golden ratio).

2, 4, 1, 5, 9, 6, 7, 14, 19, 11, 10, 17, 27, 32, 24, 12, 22, 40, 53, 45, 3, 13, 30, 61, 66, 79, 58, 37, 15, 35, 74, 87, 100, 113, 92, 16, 18, 43, 82, 121, 134, 147, 126, 71, 105, 20, 48, 95, 142, 168, 202, 181, 160, 194, 50, 23, 51, 108, 155, 189, 236, 270

Offset

1,1

Comments

Every positive integer occurs exactly once, so as a sequence, this is a permutation of the positive integers. The difference between consecutive row terms is a Fibonacci number, as is the difference between consecutive terms in column 1.

Links

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

Example

Northwest corner:
   2    4    5    7   10   12   13   15   18
   1    9   14   17   22   30   35   43   48
   6   19   27   40   61   74   82   95  108
  11   32   53   66   87  121  142  155  176
  24   45   79  100  134  168  189  223  244
   3   58  113  147  202  236  257  291  346

Mathematica

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

Crossrefs

Cf. A000045, A001622, A283738, A283740, A283741, A283746.

Sequence in context: A059573 A308437 A201283 * A080427 A118906 A085059

Adjacent sequences: A283736 A283737 A283738 * A283740 A283741 A283742

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Mar 16 2017

Status

approved