A365052 Decimal expansion of continued fraction [1; 4, 9, 16, 25, ... n^2, ... ].

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

Offset: 1

Author

Rok Cestnik, Aug 18 2023

Keywords

• nonn
• cons

Examples

			1.243288478399715644...
		

Crossrefs

Cf. A073824 (reciprocal), A036246/A036245 (convergents).

Cf. A226771, A060997, A052119.

Programs

Mathematica

A365052 = RealDigits[FromContinuedFraction[Range[1,50]^2],10,#][[1]]&;

PARI

p(N) = my(m=contfracpnqn(vector(N, i, i^2))); m[1,1]/m[2,1];
A365052(N) = {my(t=2); while(floor(10^N*p(t)) != floor(10^N*p(t+1)), t++); digits(floor(10^(N-1)*p(t)))};

Formula

Equals 1/A073824.