cp's OEIS Frontend

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.

A133472 a(n) = 10^n + 5.

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%I A133472 #32 Jun 16 2025 00:40:14
%S A133472 6,15,105,1005,10005,100005,1000005,10000005,100000005,1000000005,
%T A133472 10000000005,100000000005,1000000000005,10000000000005,
%U A133472 100000000000005,1000000000000005,10000000000000005,100000000000000005,1000000000000000005,10000000000000000005,100000000000000000005
%N A133472 a(n) = 10^n + 5.
%H A133472 Vincenzo Librandi, <a href="/A133472/b133472.txt">Table of n, a(n) for n = 0..500</a>
%H A133472 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A133472 From _R. J. Mathar_, Nov 30 2007: (Start)
%F A133472 O.g.f.: -3*(-2+17*x)/((-1+x)*(-1+10*x)) = -5/(-1+x) - 1/(-1+10*x).
%F A133472 a(n) = 10*a(n-1) - 45. (End)
%F A133472 a(n) = 10^n + 5. - _Vincenzo Librandi_, Aug 10 2011
%F A133472 From _Elmo R. Oliveira_, Jun 09 2025: (Start)
%F A133472 E.g.f.: exp(x)*(5 + exp(9*x)).
%F A133472 a(n) = 11*a(n-1) - 10*a(n-2).
%F A133472 a(n) = 3*A133473(n). (End)
%t A133472 Join[{6},Table[10*FromDigits[PadRight[{1},n,0]]+5,{n,20}]] (* or *) LinearRecurrence[{11,-10},{6,15},20] (* _Harvey P. Dale_, Sep 06 2020 *)
%o A133472 (Magma) [10^n+5: n in [0..20]]; // _Vincenzo Librandi_, Aug 10 2011
%o A133472 (PARI) apply( {A133472(n)=10^n+5}, [0..20]) \\ _M. F. Hasler_, Jun 15 2025
%Y A133472 Cf. A068128, A133384, A133473.
%K A133472 nonn,easy
%O A133472 0,1
%A A133472 _Paul Curtz_, Nov 29 2007
%E A133472 Renamed by editors, Jun 16 2025