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A226771 Decimal representation of continued fraction [1*2/2, 2*3/2, 3*4/2, 4*5/2,...], whose elements are the triangular numbers (A000217).

%I A226771 #11 Jul 29 2024 18:19:23
%S A226771 1,3,1,6,0,6,0,4,0,3,6,5,9,0,7,7,1,6,4,2,5,9,8,1,6,9,6,2,5,7,9,2,5,3,
%T A226771 9,6,1,4,9,0,9,8,1,7,8,6,2,7,2,0,9,6,9,6,7,4,4,5,6,8,2,2,6,6,9,1,7,6,
%U A226771 1,6,4,7,2,6,6,1,6,1,9,3,6,3,9,0,8,7,0,6,5,3,6,5,1,2,6,8,4,0,2,5,5,1,1,2,6
%N A226771 Decimal representation of continued fraction [1*2/2, 2*3/2, 3*4/2, 4*5/2,...], whose elements are the triangular numbers (A000217).
%C A226771 1.316060403659077164259816962579... = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,...]
%H A226771 Paolo P. Lava, <a href="/A226771/b226771.txt">Table of n, a(n) for n = 1..1000</a>
%p A226771 with(numtheory); A226771:=proc(q) local a, n; a:=(q+1)*(q+2)/2;
%p A226771 for n from q by -1 to 1 do a:=1/a+n*(n+1)/2; od;
%p A226771 print(evalf(a,1001)); end: A226771(10^4);
%t A226771 tri[n_] := n (n + 1)/2; RealDigits[ FromContinuedFraction@ tri@ Range@ 29, 10, 111] (* _Robert G. Wilson v_, Dec 26 2016 *)
%t A226771 RealDigits[FromContinuedFraction[Accumulate[Range[500]]],10,120][[1]] (* _Harvey P. Dale_, Jul 29 2024 *)
%Y A226771 Cf. A000217.
%K A226771 nonn,cons
%O A226771 1,2
%A A226771 _Paolo P. Lava_, Jun 17 2013