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A283740
Array read by antidiagonals: row k lists the numbers m such that 1/2^(k+1) < f(m) < 1/2^k, where f(m) = fractional part of m*(golden ratio).
5
1, 3, 4, 6, 7, 2, 8, 12, 10, 5, 9, 15, 23, 18, 13, 11, 20, 31, 26, 47, 68, 14, 25, 36, 39, 81, 123, 34, 16, 28, 44, 60, 102, 212, 178, 89, 17, 33, 52, 73, 136, 301, 267, 322, 466, 19, 38, 57, 94, 157, 356, 411, 699, 843, 233
OFFSET
1,2
COMMENTS
Every positive integer occurs exactly once, so that 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.
Northwest corner:
1 3 6 8 9 11 14 16
4 7 12 15 20 25 28 33
2 10 23 31 36 44 52 57
5 18 26 39 60 73 94 115
13 47 81 102 136 157 191 225
68 123 212 301 356 445 500 534
34 178 267 411 555 644 788 1021
MATHEMATICA
g = GoldenRatio; z = 50000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], 1/2^(k + 1) < t[[#]] < 1/2^k &];
s[n_] := Take[r[n], Min[20, Length[r[n]]]];
TableForm[Table[s[k], {k, 0, 10}]] (* this sequence as an array *)
w[i_, j_] := s[i][[j]]; Flatten[Table[w[n - k , k], {n, 10}, {k, n, 1, -1}]] (* this sequence *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Mar 16 2017
STATUS
approved