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Decimal expansion of sum(k>=0,sin(Pi*phi^k)) where phi=(1+sqrt(5))/2.
0

%I #9 Feb 15 2013 03:32:49

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

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

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

%N Decimal expansion of sum(k>=0,sin(Pi*phi^k)) where phi=(1+sqrt(5))/2.

%F sum(k>=0, sin(Pi*phi^k))=0.6644230370543210170957158....

%t digits = 103; $MaxExtraPrecision = digits + 30; dn = 100; Clear[f]; f[n_] := f[n] = RealDigits[ Sum[ Sin[ Pi*GoldenRatio^k], {k, 0, n}], 10, digits] // First; f[dn]; f[2*dn]; While[ f[n] != f[n - dn], n = n + dn]; f[n] (* _Jean-François Alcover_, Feb 15 2013 *)

%K cons,nonn

%O 0,1

%A _Benoit Cloitre_, Feb 27 2004