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 A097166 #55 Apr 30 2025 09:16:39
%S A097166 1,13,133,1333,13333,133333,1333333,13333333,133333333,1333333333,
%T A097166 13333333333,133333333333,1333333333333,13333333333333,
%U A097166 133333333333333,1333333333333333,13333333333333333,133333333333333333,1333333333333333333,13333333333333333333,133333333333333333333
%N A097166 Expansion of g.f. (1+2*x)/((1-x)*(1-10*x)).
%C A097166 Partial sums of (1+2*x)/(1-10*x) = {1, 12, 120, 1200, ...}.
%C A097166 Second binomial transform of A082365.
%C A097166 These terms are the x's of A070152 and the corresponding y's are A350995 (see formula and examples). - _Bernard Schott_, Feb 15 2022
%H A097166 Vincenzo Librandi, <a href="/A097166/b097166.txt">Table of n, a(n) for n = 0..200</a>
%H A097166 Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/1024-a1945-concatenations-en-tous-genres">A1945 - Concaténations en tous genres</a> (in French).
%H A097166 Richard Hoshino, <a href="https://web.archive.org/web/20150905175536/https://cms.math.ca/crux/v27/n1/public_page34-47.pdf">Astonishing Pairs of Numbers</a>, Crux Mathematicorum with Mathematical Mayhem 27:1 (2001), pp. 39-44.
%H A097166 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A097166 a(n) = (4*10^n - 1)/3.
%F A097166 a(n) = A097169(2*n).
%F A097166 a(n) = 10*a(n-1) + 3, n>0. a(n) = 11*a(n-1) - 10*a(n-2), n>1. - _Vincenzo Librandi_, Nov 01 2011
%F A097166 A350994(n) = Sum_{j=a(n)..A350995(n)} = a(n).A350995(n) where "." means concatenation. - _Bernard Schott_, Jan 28 2022
%F A097166 From _Elmo R. Oliveira_, Apr 29 2025: (Start)
%F A097166 E.g.f.: exp(x)*(4*exp(9*x) - 1)/3.
%F A097166 a(n) = A198970(n)/3. (End)
%e A097166 a(0) = (4-1)/3 = 1 and Sum_{j=1..5} = 15.
%e A097166 a(1) = (40-1)/3 = 13 and Sum_{j=13..53} = 1353.
%e A097166 a(2) = (400-1)/3 = 133 and Sum_{j=133..533} = 133533.
%p A097166 a:= n-> parse(cat(1, 3$n)):
%p A097166 seq(a(n), n=0..18); # _Alois P. Heinz_, Aug 23 2019
%t A097166 NestList[10#+3&,1,20] (* _Harvey P. Dale_, Jan 22 2014 *)
%o A097166 (Magma) [(4*10^n-1)/3 : n in [0..20]]; // _Vincenzo Librandi_, Nov 01 2011
%o A097166 (Python) [(4*10**n-1)//3 for n in range(25)] # _Gennady Eremin_, Mar 04 2022
%Y A097166 Cf. A056698 (index of primes), A082365, A097169, A309907 (squares of this).
%Y A097166 Cf. A070152, A070153, A186074, A198970, A350994, A350995.
%K A097166 nonn,easy
%O A097166 0,2
%A A097166 _Paul Barry_, Jul 30 2004