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Decimal expansion of 1/sqrt(1 + 1/sqrt(2 + 1/sqrt(3 + 1/sqrt(4 + 1/sqrt(5 + ...))))).
1

%I #10 Oct 11 2018 17:33:51

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

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

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

%N Decimal expansion of 1/sqrt(1 + 1/sqrt(2 + 1/sqrt(3 + 1/sqrt(4 + 1/sqrt(5 + ...))))).

%H G. C. Greubel, <a href="/A296140/b296140.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFractionConstants.html">Continued Fraction Constants</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NestedRadicalConstant.html">Nested Radical Constant</a>

%e 0.7837663092363964699519430776387428127041411807738774755...

%t RealDigits[Fold[1/Sqrt[#1 + #2]&, 0, Range[100, 1, -1]], 10, 100][[1]] (* _Jean-François Alcover_, Dec 19 2017 *)

%Y Cf. A052119, A060006, A072449.

%K nonn,cons

%O 0,1

%A _Ilya Gutkovskiy_, Dec 05 2017