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A161484 Decimal expansion of (187 + 78*sqrt(2))/151.

%I A161484 #17 Aug 23 2025 12:32:13
%S A161484 1,9,6,8,9,3,1,5,0,9,0,4,0,4,0,6,7,1,3,9,5,0,5,4,1,1,9,5,2,8,7,1,2,8,
%T A161484 8,0,8,7,9,7,5,7,8,8,4,9,5,3,2,4,6,3,2,4,3,0,9,7,8,8,7,5,4,6,7,7,6,6,
%U A161484 6,9,7,5,7,0,8,6,3,8,6,4,1,7,4,1,9,4,0,5,4,8,1,3,0,8,3,1,8,1,6,3,3,9,9,5,4
%N A161484 Decimal expansion of (187 + 78*sqrt(2))/151.
%C A161484 Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A161482.
%C A161484 Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A161483.
%H A161484 G. C. Greubel, <a href="/A161484/b161484.txt">Table of n, a(n) for n = 1..10000</a>
%F A161484 Equals (13 + 3*sqrt(2))/(13 - 3*sqrt(2)).
%F A161484 Minimal polynomial: 151*x^2 - 374*x + 151. - _Stefano Spezia_, Aug 23 2025
%e A161484 (187 + 78*sqrt(2))/151 = 1.96893150904040671395...
%p A161484 with(MmaTranslator[Mma]): Digits:=150:
%p A161484 RealDigits(evalf((187+78*sqrt(2))/151))[1]; # _Muniru A Asiru_, Apr 08 2018
%t A161484 RealDigits[(187+78Sqrt[2])/151,10,120][[1]] (* _Harvey P. Dale_, Apr 29 2011 *)
%o A161484 (PARI) (187 + 78*sqrt(2))/151 \\ _G. C. Greubel_, Apr 07 2018
%o A161484 (Magma) (187 + 78*Sqrt(2))/151; // _G. C. Greubel_, Apr 07 2018
%Y A161484 Cf. A161482, A161483, A002193 (decimal expansion of sqrt(2)), A161485 (decimal expansion of (24723+6758*sqrt(2))/151^2).
%K A161484 nonn,cons,easy
%O A161484 1,2
%A A161484 _Klaus Brockhaus_, Jun 13 2009