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A163662 A020988 written in base 2.

%I A163662 #26 Jul 23 2025 17:10:37
%S A163662 10,1010,101010,10101010,1010101010,101010101010,10101010101010,
%T A163662 1010101010101010,101010101010101010,10101010101010101010,
%U A163662 1010101010101010101010,101010101010101010101010,10101010101010101010101010,1010101010101010101010101010,101010101010101010101010101010
%N A163662 A020988 written in base 2.
%C A163662 The digits are n concatenated blocks of (10).
%C A163662 Smallest number having alternating bit sum -n. Cf. A065359. - _Washington Bomfim_, Jan 22 2011
%H A163662 G. C. Greubel, <a href="/A163662/b163662.txt">Table of n, a(n) for n = 1..495</a>
%H A163662 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A163662 a(n) = Sum_{k=1..n} 10^(2*k-1).
%F A163662 From _R. J. Mathar_, Jul 08 2009: (Start)
%F A163662 a(n) = 100*a(n-1) + 10.
%F A163662 a(n) = 101*a(n-1) - 100*a(n-2).
%F A163662 G.f.: 10*x/((100*x-1)*(x-1)). (End)
%F A163662 From _G. C. Greubel_, Aug 01 2017: (Start)
%F A163662 a(n) = (10/99)*(10^(2*n) - 1).
%F A163662 E.g.f.: (10/99)*(exp(100*x) - exp(x)). (End)
%F A163662 a(n) = 10*A094028(n-1). - _Elmo R. Oliveira_, Jul 23 2025
%p A163662 A163662 := proc(n) add(10^(2*k-1),k=1..n) ; end: seq(A163662(n),n=1..30) ; # _R. J. Mathar_, Jul 08 2009
%t A163662 Table[(10/99)*(10^(2*n) - 1), {n,1,50}] (* _G. C. Greubel_, Aug 01 2017 *)
%t A163662 Table[FromDigits[PadRight[{},2n,{1,0}]],{n,20}] (* or *) LinearRecurrence[ {101,-100},{10,1010},20] (* _Harvey P. Dale_, Jan 08 2020 *)
%o A163662 (PARI) x='x+O('x^50); Vec(10*x/((100*x-1)*(x-1))) \\ _G. C. Greubel_, Aug 01 2017
%Y A163662 Cf. A065359, A094028.
%K A163662 nonn,base,easy
%O A163662 1,1
%A A163662 _Jaroslav Krizek_, Aug 02 2009