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%I A139345 #22 Feb 07 2022 02:52:25
%S A139345 9,9,8,8,8,4,5,0,9,0,9,4,8,8,4,7,9,8,8,3,3,2,6,8,2,4,2,6,3,0,1,2,9,0,
%T A139345 4,4,6,3,8,6,5,1,1,9,2,1,2,7,0,5,7,4,4,3,4,5,5,3,9,9,6,6,8,8,1,0,7,1,
%U A139345 8,2,3,9,1,8,2,7,9,9,5,4,0,9,2,6,6,8,5,3,3,6,0,4,0,4,4,6,0,2,7,1,8,5,2,1
%N A139345 Decimal expansion of sine of the golden ratio. That is, the decimal expansion of sin((1+sqrt(5))/2).
%C A139345 By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 13 2019
%H A139345 Mohammad K. Azarian, <a href="https://doi.org/10.35834/1998/1003176">Problem 123</a>, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3 (Fall 1998), p. 176; <a href="https://doi.org/10.35834/2000/1201050">Solution</a>, ibid., Vol. 12, No. 1 (Winter 2000), pp. 61-62.
%H A139345 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A139345 Equals sin(A001622).
%F A139345 Equals 1/A139350. - _Amiram Eldar_, Feb 07 2022
%e A139345 0.99888450909488479883326824263012904463865119212705...
%t A139345 RealDigits[Sin[GoldenRatio], 10, 100][[1]] (* _Amiram Eldar_, Feb 07 2022 *)
%o A139345 (PARI) sin((1+sqrt(5))/2) \\ _Charles R Greathouse IV_, May 13 2019
%Y A139345 Cf. A001622, A094214, A104457, A098317, A002390, A139339, A139340, A139341, A139342, A139350.
%K A139345 nonn,cons
%O A139345 0,1
%A A139345 _Mohammad K. Azarian_, Apr 15 2008
%E A139345 Leading zero removed by _R. J. Mathar_, Feb 05 2009

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