A283738 - OEIS

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).

%I #15 Aug 02 2021 02:39:47

%S 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,

%T 65,86,52,16,41,70,78,99,120,107,18,17,46,83,91,133,175,141,73,39,19,

%U 54,96,112,154,230,196,162,128,94,21,59,104,146,188,264,251

%N 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).

%C A permutation of the positive integers.

%C 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.

%F Northwest corner:

%F 1 3 6 8 9 11 14 16 17

%F 4 12 20 25 33 38 41 46 54

%F 7 15 28 49 62 70 83 96 104

%F 2 23 36 57 78 91 112 146 167

%F 10 44 65 99 133 154 188 209 243

%F 31 86 120 175 230 264 319 353 374

%t g = GoldenRatio; z = 5000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];

%t r[k_] := Select[Range[z], 1/(k + 1) < t[[#]] < 1/k &];

%t s[n_] := Take[r[n], Min[20, Length[r[n]]]];

%t TableForm[Table[s[k], {k, 1, 14}]] (* A283738, array *)

%t w[i_, j_] := s[i][[j]]; Flatten[Table[w[n - k + 1, k], {n, 14}, {k, n, 1, -1}]] (* A283738, sequence *)

%Y Cf. A000045, A001622, A283739, A283740, A283741, A283745.

%K nonn,tabl,easy

%O 1,2

%A _Clark Kimberling_, Mar 16 2017