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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).
4
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.
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
nonn,tabl,easy
AUTHOR
Clark Kimberling, Mar 16 2017
STATUS
approved