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

1,2

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

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 *)

Crossrefs

Cf. A000217.

Sequence in context: A174424 A298330 A210621 * A096614 A011002 A298241

Adjacent sequences: A226768 A226769 A226770 * A226772 A226773 A226774

Keyword

nonn,cons

Author

Paolo P. Lava, Jun 17 2013

Status

approved