(MAGMAMagma) (19491+12070*Sqrt(2))/97^2; // G. C. Greubel, Mar 30 2018

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with(MmaTranslator[Mma]): Digits:=100:

RealDigits(evalf((19491+12070*sqrt(2))/97^2))[1]; # Muniru A Asiru, Mar 31 2018

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G. C. Greubel, <a href="/A157471/b157471.txt">Table of n, a(n) for n = 1..10000</a>

RealDigits[(19491+12070*Sqrt[2])/97^2, 10, 100][[1]] (* G. C. Greubel, Mar 30 2018 *)

(PARI) (19491+12070*sqrt(2))/97^2 \\ G. C. Greubel, Mar 30 2018

(MAGMA) (19491+12070*Sqrt(2))/97^2; // G. C. Greubel, Mar 30 2018

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editing

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Mar 12 2009

Decimal expansion of (19491+12070*sqrt(2))/97^2.

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

1,1

lim_{n -> infinity} b(n)/b(n-1) = (19491+12070*sqrt(2))/97^2 for n mod 3 = 0, b = A129836.

lim_{n -> infinity} b(n)/b(n-1) = (19491+12070*sqrt(2))/97^2 for n mod 3 = 1, b = A157469.

(19491+12070*sqrt(2))/97^2 = (170+71*sqrt(2))/(170-71*sqrt(2))

= (3+2*sqrt(2))*(14-sqrt(2))^2/(14+sqrt(2))^2.

(19491+12070*sqrt(2))/97^2 = 3.88570067997058744170...

Cf. A129836, A157469, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A157470 (decimal expansion of (99+14*sqrt(2))/97).

cons,nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 12 2009

approved