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A194375
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Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(5) and < > denotes fractional part.
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3
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1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74
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OFFSET
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1,2
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COMMENTS
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See A194368.
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LINKS
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Table of n, a(n) for n=1..69.
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MATHEMATICA
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r = Sqrt[5]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 500}];
Flatten[Position[t1, 1]] (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]] (* A194374 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194375 *)
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CROSSREFS
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Cf. A194368, A194375.
Sequence in context: A098572 A001955 A184480 * A188222 A329990 A109237
Adjacent sequences: A194372 A194373 A194374 * A194376 A194377 A194378
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Aug 23 2011
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STATUS
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approved
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