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A283746
a(n) = least m such that (n-1)/n < f(m) < n/(n+1), where f(m) = fractional part of m*(golden ratio).
3
2, 1, 6, 11, 24, 3, 37, 16, 105, 50, 84, 29, 118, 207, 63, 152, 8, 241, 97, 330, 186, 419, 42, 275, 508, 131, 741, 364, 597, 220, 830, 453, 76, 686, 1296, 309, 919, 1529, 542, 165, 1762, 775, 1385, 398, 1008, 21, 1618, 631, 2228, 1241, 254, 1851, 864, 2461
OFFSET
1,1
COMMENTS
This is column 1 of A283739; |a(n+1)-a(n)| is a Fibonacci number for n>=1.
MATHEMATICA
g = GoldenRatio; z = 10000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], (k - 1)/k < t[[#]] < k/(k + 1) &, 1];
Flatten[Table[r[k], {k, 1, 200}]] (* A283746 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 17 2017
STATUS
approved