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A050621 Smallest n-digit number divisible by 2^n. 25

%I

%S 2,12,104,1008,10016,100032,1000064,10000128,100000256,1000000512,

%T 10000001024,100000002048,1000000004096,10000000008192,

%U 100000000016384,1000000000032768,10000000000065536,100000000000131072

%N Smallest n-digit number divisible by 2^n.

%C Quotients arising from this sequence give A034478 ((5^(n-1)+1)/2).

%H Vincenzo Librandi, <a href="/A050621/b050621.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (12,-20).

%F a(n) = 10^(n-1) + 2^(n-1).

%F G.f.: Q(0) where Q(k)= 1 + 5^k/(1 - 2*x/(2*x + 5^k/Q(k+1) )); (continued fraction ). - _Sergei N. Gladkovskii_, Apr 10 2013

%F G.f.: 2*x*(1-6*x)/((1-2*x)*(1-10*x)). - _Vincenzo Librandi_, Sep 12 2014

%F a(n) = 12*a(n-1) - 20*a(n-2) for n>1. - _Vincenzo Librandi_, Sep 12 2014

%t CoefficientList[Series[2 (1 - 6 x)/((1 - 2 x) (1 - 10 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Sep 12 2014 *)

%o (MAGMA) [2^(n-1)+10^(n-1): n in [1..21]]; // _Vincenzo Librandi_, Sep 12 2014

%o (PARI) a(n) = 10^(n-1) + 2^(n-1) \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Cf. A035014, A034478, A050622.

%K nonn,base,easy

%O 1,1

%A _Patrick De Geest_, Jun 15 1999

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Last modified December 11 06:55 EST 2016. Contains 279043 sequences.