A299639 - OEIS

%I #6 Apr 08 2018 20:11:28

%S 0,4,5,52168,52878,53588,54298,55008,55718,56428,57138,57848,58558,

%T 59268,59978,60688,61398,62108,62818,63528,64238,64948,65658,66368,

%U 67078,67788,68498,69208,69918,70628,71338,72048,72758,73468,74178,74888,75598,76308

%N 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).

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

%e Records for n - 0,1,2, read from the first 6 values of d(n) approximated by

%e 0.381, -0.088, -1.34, -0.56, 0.73, 1.35; viz.,

%e d(0) = cos(1) + sin(1) - cos(0) - sin(0) = 0.38177...

%e d(4) = cos(5) + sin(5) - cos(4) - sin(4) = 0.73518...

%e d(5) = 1.356016878...

%e d(52168) = 1.356016794...

%t z = 100000; d[n_] := N[Cos[n + 1] + Sin[n + 1] - Cos[n] - Sin[n], 10];

%t max = d[0]; k = 0; s = {0};

%t While[k < z, a = d[k]; If[a > max, max = a; AppendTo[s, k]]; k++]; s

%Y Cf. A299640.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Apr 08 2018