A283741 Array read by descending antidiagonals: row k lists the numbers m such that 1/2^(k+1) < 1 - f(m) < 1/2^k, where f(m) is the fractional part of m*(golden ratio).

2, 4, 1, 5, 6, 3, 7, 9, 11, 16, 10, 14, 24, 29, 8, 12, 17, 32, 50, 42, 21, 13, 19, 37, 63, 97, 76, 55, 15, 22, 45, 71, 131, 110, 199, 288, 18, 27, 53, 84, 152, 165, 343, 521, 144, 20, 30, 58, 105, 186, 254, 432, 665, 754, 377

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..55.

Index entries for sequences that are permutations of the natural numbers

Example

Upper-left corner:
   2    4    5    7   10   12   13   15 ...
   1    6    9   14   17   19   22   27 ...
   3   11   24   32   37   45   53   58 ...
  16   29   50   63   71   84  105  118 ...
   8   42   97  131  152  186  220  241 ...
  21   76  110  165  254  309  398  453 ...
  ...

Mathematica

g = GoldenRatio; z = 50000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], (2^k - 1)/2^k < t[[#]] < (2*2^k - 1)/2^(k + 1) &];
s[n_] := Take[r[n], Min[20, Length[r[n]]]];
TableForm[Table[s[k], {k, 0, 10}]] (* A283741, array *)
w[i_, j_] := s[i][[j]]; Flatten[Table[w[n - k , k], {n, 10}, {k, n, 1, -1}]]  (* A283741, sequence *)

Crossrefs

Cf. A000045, A001622, A283738, A283739, A283740.

Sequence in context: A165064 A299918 A021418 * A094640 A070937 A278437

Adjacent sequences: A283738 A283739 A283740 * A283742 A283743 A283744

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Mar 16 2017

Extensions

Name corrected by Jon E. Schoenfield, Mar 25 2017

Status

approved