A283740 Array read by antidiagonals: row k lists the numbers m such that 1/2^(k+1) < f(m) < 1/2^k, where f(m) = fractional part of m*(golden ratio).

1, 3, 4, 6, 7, 2, 8, 12, 10, 5, 9, 15, 23, 18, 13, 11, 20, 31, 26, 47, 68, 14, 25, 36, 39, 81, 123, 34, 16, 28, 44, 60, 102, 212, 178, 89, 17, 33, 52, 73, 136, 301, 267, 322, 466, 19, 38, 57, 94, 157, 356, 411, 699, 843, 233

Offset

1,2

Comments

Every positive integer occurs exactly once, so that 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.

Northwest corner:

1 3 6 8 9 11 14 16

4 7 12 15 20 25 28 33

2 10 23 31 36 44 52 57

5 18 26 39 60 73 94 115

13 47 81 102 136 157 191 225

68 123 212 301 356 445 500 534

34 178 267 411 555 644 788 1021

Links

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

Mathematica

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

Crossrefs

Cf. A000045, A001622, A283738, A283739, A283741.

Sequence in context: A070737 A225647 A135599 * A167161 A129000 A260158

Adjacent sequences: A283737 A283738 A283739 * A283741 A283742 A283743

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Mar 16 2017

Status

approved