This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274743 #61 Aug 05 2024 10:07:28
%S A274743 99,10989,1099989,109999989,10999999989,1099999999989,109999999999989,
%T A274743 10999999999999989,1099999999999999989,109999999999999999989,
%U A274743 10999999999999999999989,1099999999999999999999989,109999999999999999999999989,10999999999999999999999999989
%N A274743 Repunits with odd indices multiplied by 99, i.e., 99*(1, 111, 11111, 1111111, ...).
%C A274743 It is apparent that the reciprocals of the terms in the sequence give an increasing sequence of periodic terms similar to A095372, but with the initial term equal to "01". The leading zero is important (see links). Furthermore, the reciprocals of the terms give a sequence of even growing periods, starting from 2, with delta = 4 (i.e., 2, 6, 10, 14, 18, ...).
%C A274743 Adding "11" to each term gives the binary representation of the n-th iteration of "Rule 14" elementary cellular automaton starting with a single ON (black cell) as in A266299.
%H A274743 Rodolfo 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 A274743 Rodolfo 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 A274743 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A274743 a(n) = 101*a(n-1) - 100*a(n-2) for n>2, with a(0)= 99 and a(1)= 10989.
%F A274743 a(n) = 99*A100706(n-1).
%F A274743 G.f.: 99*x*(1 + 10*x)/((1 - x)*(1 - 100*x)). - _Ilya Gutkovskiy_, Jul 04 2016
%F A274743 a(n) = 11*(10^(2*n-1)-1). - _Wesley Ivan Hurt_, Jul 04 2016
%F A274743 E.g.f.: 11*(9 - 10*exp(x) + exp(100*x))/10. - _Stefano Spezia_, Aug 05 2024
%e A274743 a(2) = 101*10989 - 100*99 = 1099989.
%p A274743 A274743:=n->11*(10^(2*n-1)-1): seq(A274743(n), n=1..20); # _Wesley Ivan Hurt_, Jul 04 2016
%t A274743 Array[99(10^(2 # - 1) - 1)/9 &, 15] (* _Michael De Vlieger_, Jul 04 2016 *)
%t A274743 99*Table[FromDigits[PadRight[{},2n+1,1]],{n,0,15}] (* _Harvey P. Dale_, Jul 22 2019 *)
%o A274743 (Magma) [11*(10^(2*n-1)-1) : n in [1..20]]; // _Wesley Ivan Hurt_, Jul 04 2016
%o A274743 (PARI) Vec(99*x*(1+10*x)/((1-x)*(1-100*x)) + O(x^99)) \\ _Altug Alkan_, Jul 05 2016
%o A274743 (PARI) a002275(n) = (10^n-1)/9
%o A274743 a(n) = 99*a002275(2*n-1) \\ _Felix Fröhlich_, Jul 05 2016
%Y A274743 Cf. A002275, A095372, A100706, A266299, A274755.
%K A274743 nonn,easy
%O A274743 1,1
%A A274743 _Rodolfo A. Fiorini_, Jul 04 2016