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).

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, 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, 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

Offset: 1

Author

Paolo P. Lava, Jun 17 2013

Keywords

• nonn
• cons

Comments

1.316060403659077164259816962579... = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,...]

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217.

Programs

Maple

with(numtheory); A226771:=proc(q) local a, n; a:=(q+1)*(q+2)/2;
for n from q by -1 to 1 do a:=1/a+n*(n+1)/2; od;
print(evalf(a,1001)); end: A226771(10^4);

Mathematica

tri[n_] := n (n + 1)/2; RealDigits[ FromContinuedFraction@ tri@ Range@ 29, 10, 111] (* Robert G. Wilson v, Dec 26 2016 *)
RealDigits[FromContinuedFraction[Accumulate[Range[500]]],10,120][[1]] (* Harvey P. Dale, Jul 29 2024 *)