A299639 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, 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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..37.

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(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...

Mathematica

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

Crossrefs

Cf. A299640.

Sequence in context: A270975 A058916 A064612 * A244444 A231407 A005927

Adjacent sequences: A299636 A299637 A299638 * A299640 A299641 A299642

Keyword

nonn,easy

Author

Clark Kimberling, Apr 08 2018

Status

approved