A299640 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).

0, 1, 2, 8, 27, 360, 51813, 52523, 53233, 53943, 54653, 55363, 56073, 56783, 57493, 58203, 58913, 59623, 60333, 61043, 61753, 62463, 63173, 63883, 64593, 65303, 66013, 66723, 67433, 68143, 68853, 69563, 70273, 70983, 71693, 72403, 73113, 73823, 74533, 75243

Offset

0,3

Comments

Conjecture: d(n) -> -1.356...

Links

Table of n, a(n) for n=0..39.

Example

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(1) = cos(1) + sin(1) - cos(0) - sin(0) = 0.3817732907...
d(2) = -0.8886227004...
d(8) = -1.342023079...
d(27) = -1.342869989...

Mathematica

z = 100000; d[n_] := N[Cos[n + 1] + Sin[n + 1] - Cos[n] - Sin[n], 10];
min = d[0]; k = 0; s = {0};
While[k < z, a = d[k]; If[a < min, min = a; AppendTo[s, k]]; k++]; s
d[s]

Crossrefs

Cf. A299639.

Sequence in context: A276940 A287204 A391918 * A197932 A170871 A390153

Adjacent sequences: A299637 A299638 A299639 * A299641 A299642 A299643

Keyword

nonn,easy

Author

Clark Kimberling, Apr 08 2018

Status

approved