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.
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
KEYWORD
AUTHOR
Clark Kimberling, Mar 16 2017
STATUS
approved