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%I #11 Oct 03 2023 22:23:12
%S 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,
%T 79,58,37,15,35,74,87,100,113,92,16,18,43,82,121,134,147,126,71,105,
%U 20,48,95,142,168,202,181,160,194,50,23,51,108,155,189,236,270
%N 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).
%C 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.
%e Northwest corner:
%e 2 4 5 7 10 12 13 15 18
%e 1 9 14 17 22 30 35 43 48
%e 6 19 27 40 61 74 82 95 108
%e 11 32 53 66 87 121 142 155 176
%e 24 45 79 100 134 168 189 223 244
%e 3 58 113 147 202 236 257 291 346
%t g = GoldenRatio; z = 5000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
%t r[k_] := Select[Range[z], (k-1)/k < t[[#]] < k/(k+1) &];
%t s[n_] := Take[r[n], Min[20, Length[r[n]]]];
%t TableForm[Table[s[k], {k, 1, 14}]] (* this sequence as an array *)
%t w[i_, j_] := s[i][[j]]; Flatten[Table[w[n - k + 1, k], {n, 14}, {k, n, 1, -1}]] (* this sequence *)
%Y Cf. A000045, A001622, A283738, A283740, A283741, A283746.
%K nonn,tabl,easy
%O 1,1
%A _Clark Kimberling_, Mar 16 2017
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