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Decimal expansion of 10^(3/4).
1

%I #27 Oct 26 2024 04:43:47

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

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

%U 3,5,6,8,6,4,3,0,6,2,8,4,8,9,0,5,8,5,7,9,8,4,5,2,6,2,2,0,3,0

%N Decimal expansion of 10^(3/4).

%C This number is the geometric mean of sqrt(10) and 10.

%C Floor(10^((4*n - 1)/4)) = A018072(4*n - 1) can be obtained by multiplying this number by 10^(n - 1) and truncating the decimal places.

%C Harriot gives this constant to 18 decimal places. - _Charles R Greathouse IV_, Oct 22 2014

%D P. H. Underwood, "Logarithms" Texas Mathematics Teachers' Bulletin, Vol 6 No. 1 (1920), p. 23.

%H Thomas Harriot, <a href="http://echo.mpiwg-berlin.mpg.de/MPIWG:5PYT50NY">Manuscript 6782</a>, <a href="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?tocMode=thumbs&amp;tocPN=1&amp;url=/mpiwg/online/permanent/library/HSPGZ0AE/&amp;viewMode=image&amp;start=10&amp;searchPN=1&amp;characterNormalization=reg&amp;query=&amp;queryType=&amp;pn=13">p. 7</a>, c. 1599.

%e 5.6234132519034908039495103977648...

%t RealDigits[10^(3/4), 10, 105][[1]]

%o (PARI) 10^.75 \\ _Charles R Greathouse IV_, Oct 22 2014

%Y Cf. A010467, A011007.

%K nonn,cons,easy

%O 1,1

%A _Alonso del Arte_, Jan 27 2013