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a(n) is the largest integer whose cube has n digits and first digit 1, except that a(2)=2.
3

%I #30 Aug 01 2019 00:06:48

%S 1,2,5,12,27,58,125,271,584,1259,2714,5848,12599,27144,58480,125992,

%T 271441,584803,1259921,2714417,5848035,12599210,27144176,58480354,

%U 125992104,271441761,584803547,1259921049,2714417616,5848035476

%N a(n) is the largest integer whose cube has n digits and first digit 1, except that a(2)=2.

%C a(2)=2 because there is no integer with cube between 10 and 19.

%C A generalization to arbitrary powers is found in Hürlimann, 2004.

%H W. Hürlimann, <a href="http://www.ijpam.eu/contents/2004-11-1/4/4.pdf">Integer powers and Benford's law</a>, International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 39-46, 2004.

%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>

%F a(n) = floor((10^n/5)^(1/3)).

%t Floor[Power[(10^Range[30])/5, (3)^-1]] (* _Harvey P. Dale_, Jul 15 2011 *)

%Y Cf. A061439, A083377, A083379, A083380.

%K base,easy,nonn

%O 1,2

%A Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

%E Edited by _Don Reble_, Nov 05 2005