cp's OEIS Frontend

A274755 Repunits with even indices multiplied by 99, i.e., 99*(11, 1111, 111111, 11111111, ...).

%I A274755 #40 Jun 10 2025 01:14:28
%S A274755 1089,109989,10999989,1099999989,109999999989,10999999999989,
%T A274755 1099999999999989,109999999999999989,10999999999999999989,
%U A274755 1099999999999999999989,109999999999999999999989,10999999999999999999999989,1099999999999999999999999989
%N A274755 Repunits with even indices multiplied by 99, i.e., 99*(11, 1111, 111111, 11111111, ...).
%C A274755 The reciprocals of the terms give a sequence of even growing periods, starting from 22, with delta = 22 (i.e., 22,44,66,88,110,132,...).
%H A274755 R. A. Fiorini, <a href="http://dx.doi.org/10.3233/FI-2014-1116">How Random is Your Tomographic Noise? A Number Theoretic Transform (NTT) Approach</a>, Fundamenta Informaticae, 135(1-2), 2014, 135-170.
%H A274755 R. A. Fiorini, <a href="http://dx.doi.org/10.3233/FI-2015-1267">Computerized tomography noise reduction by CICT optimized exponential cyclic sequences (OECS) co-domain</a>, Fundamenta Informaticae, vol.141 (2015), 115-134.
%H A274755 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A274755 a(n) = 101*a(n-1) - 100*a(n-2), with a(1)= 1089 and a(2)= 109989.
%F A274755 G.f.: 1089*x/((1 - x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Jul 04 2016
%F A274755 a(n) = 99*A099814(n). - _Michel Marcus_, Jul 04 2016
%F A274755 a(n) = 11*(10^(2*n)-1). - _Robert Israel_, Jul 06 2016
%F A274755 E.g.f.: 11*exp(x)*(exp(99*x) - 1). - _Elmo R. Oliveira_, Jun 09 2025
%e A274755 a(3) = 101*109989 - 100*1089 = 10999989.
%p A274755 A274755:= n-> 11*(10^(2*n) - 1) : seq(A274755(n), n=1..20);
%t A274755 Array[99(10^(2 #)- 1)/9&, 15]
%t A274755 LinearRecurrence[{101, -100}, {1089, 109989}, 20] (* _Vincenzo Librandi_, Jul 07 2016 *)
%o A274755 (Magma) [11*(10^(2*n) - 1): n in [1..20]];
%o A274755 (PARI) Vec(1089*x/((1-x)*(1-100*x)) + O(x^99)) \\ _Altug Alkan_, Jul 06 2016
%Y A274755 Cf. A002275, A099814, A274743.
%K A274755 nonn,easy
%O A274755 1,1
%A A274755 _Rodolfo A. Fiorini_, Jul 04 2016