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A283738
Array read by antidiagonals: row k shows the numbers m such that 1/(k+1) < f(m) < 1/k, where f(m) = fractional part of m*(golden ratio).
5
1, 3, 4, 6, 12, 7, 8, 20, 15, 2, 9, 25, 28, 23, 10, 11, 33, 49, 36, 44, 31, 14, 38, 62, 57, 65, 86, 52, 16, 41, 70, 78, 99, 120, 107, 18, 17, 46, 83, 91, 133, 175, 141, 73, 39, 19, 54, 96, 112, 154, 230, 196, 162, 128, 94, 21, 59, 104, 146, 188, 264, 251
OFFSET
1,2
COMMENTS
A permutation of the positive integers.
The difference between any two consecutive terms in any row is a Fibonacci number, as is the difference between any two consecutive terms in column 1.
FORMULA
Northwest corner:
1 3 6 8 9 11 14 16 17
4 12 20 25 33 38 41 46 54
7 15 28 49 62 70 83 96 104
2 23 36 57 78 91 112 146 167
10 44 65 99 133 154 188 209 243
31 86 120 175 230 264 319 353 374
MATHEMATICA
g = GoldenRatio; z = 5000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], 1/(k + 1) < t[[#]] < 1/k &];
s[n_] := Take[r[n], Min[20, Length[r[n]]]];
TableForm[Table[s[k], {k, 1, 14}]] (* A283738, array *)
w[i_, j_] := s[i][[j]]; Flatten[Table[w[n - k + 1, k], {n, 14}, {k, n, 1, -1}]] (* A283738, sequence *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Mar 16 2017
STATUS
approved