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
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
KEYWORD
AUTHOR
Clark Kimberling, Mar 16 2017
EXTENSIONS
Name corrected by Jon E. Schoenfield, Mar 25 2017
STATUS
approved