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A299639
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a(0) = 0, and for n > 0, (a(n)) gives the indices n for which d(n) > d(k) for k < n, where d is the difference sequence of (cos k + sin k).
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1
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0, 4, 5, 52168, 52878, 53588, 54298, 55008, 55718, 56428, 57138, 57848, 58558, 59268, 59978, 60688, 61398, 62108, 62818, 63528, 64238, 64948, 65658, 66368, 67078, 67788, 68498, 69208, 69918, 70628, 71338, 72048, 72758, 73468, 74178, 74888, 75598, 76308
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OFFSET
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0,2
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COMMENTS
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Conjecture: d(n) -> 1.356...
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LINKS
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EXAMPLE
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Records for n - 0,1,2, read from the first 6 values of d(n) approximated by
0.381, -0.088, -1.34, -0.56, 0.73, 1.35; viz.,
d(0) = cos(1) + sin(1) - cos(0) - sin(0) = 0.38177...
d(4) = cos(5) + sin(5) - cos(4) - sin(4) = 0.73518...
d(5) = 1.356016878...
d(52168) = 1.356016794...
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MATHEMATICA
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z = 100000; d[n_] := N[Cos[n + 1] + Sin[n + 1] - Cos[n] - Sin[n], 10];
max = d[0]; k = 0; s = {0};
While[k < z, a = d[k]; If[a > max, max = a; AppendTo[s, k]]; k++]; s
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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