A365052 - OEIS

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A365052

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

1

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..100.

FORMULA

Equals 1/A073824.

EXAMPLE

1.243288478399715644...

MATHEMATICA

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

PROG

(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)))};

CROSSREFS

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

Cf. A226771, A060997, A052119.

Sequence in context: A368519 A059908 A084936 * A308744 A216842 A099066

Adjacent sequences: A365049 A365050 A365051 * A365053 A365054 A365055

KEYWORD

nonn,cons

AUTHOR

Rok Cestnik, Aug 18 2023

STATUS

approved