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Decimal expansion of the least x>0 that gives the absolute minimum of Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x), where f(x)=sin(x)+cos(x).
3

%I #6 Mar 30 2012 18:57:55

%S 5,2,9,4,4,2,8,9,4,6,9,5,2,1,1,7,6,4,0,5,6,0,5,3,3,3,9,7,0,4,6,4,5,0,

%T 0,7,5,7,3,6,7,8,3,8,6,1,9,5,4,9,3,1,8,1,4,1,4,2,6,2,3,9,6,5,8,2,1,1,

%U 4,9,9,8,0,5,4,5,8,4,0,5,7,2,3,6,3,3,9,6,8,6,2,5,9,9,6,2,8,7,8

%N Decimal expansion of the least x>0 that gives the absolute minimum of Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x), where f(x)=sin(x)+cos(x).

%C See A198735 for a guide to related sequences.

%e x=5.2944289469521176405605333970464500...

%e min=-2.75873119163855400111893535814922666...

%t f[t_] := Sin[t] + Cos[t]

%t n = 3; s[t_] := Sum[f[k*t], {k, 1, n}]

%t x = N[Minimize[s[t], t], 110]; u = Part[x, 1]

%t v = t /. Part[x, 2]

%t RealDigits[u] (* A198737 *)

%t RealDigits[v] (* A198738 *)

%t Plot[s[t], {t, -3 Pi, 3 Pi}]

%Y Cf. A198735.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011