A347052 Decimal expansion of the continued fraction 1/(1*2 + 1/(2*3 + 1/(3*4 + 1/(4*5 + 1/(5*6 + ...))))).

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

Offset: 0

Author

Ilya Gutkovskiy, Aug 13 2021

Keywords

• nonn
• cons
• changed

Examples

			0.46202332508023861850355914941757191597703...
		

Crossrefs

Cf. A002378, A052119, A073823, A073824, A346960, A347051.

Programs

Mathematica

terms=106; RealDigits[ContinuedFractionK[k(k+1),{k,terms}],10,terms][[1]] (* Stefano Spezia, Aug 23 2025 *)

Formula

Equals lim_{n -> oo} A346960(n)/A347051(n).