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.

A123522 Not of the form n + [log_10 n].

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%I A123522 #25 Sep 08 2022 08:45:28
%S A123522 0,10,101,1002,10003,100004,1000005,10000006,100000007,1000000008,
%T A123522 10000000009,100000000010,1000000000011,10000000000012,
%U A123522 100000000000013,1000000000000014,10000000000000015,100000000000000016
%N A123522 Not of the form n + [log_10 n].
%C A123522 Smallest number such that (sum of digits) mod (number of digits) = n in decimal representation. - _Reinhard Zumkeller_, Aug 15 2010
%C A123522 Consider a word on the alphabet {0,1,2,...,9} that has length of 10^a(n).  The expected number of occurrences of a pattern (contiguous subsequence) p_1,p_2,...p_n for all such words is 1. - _Geoffrey Critzer_, Feb 03 2012
%H A123522 G. C. Greubel, <a href="/A123522/b123522.txt">Table of n, a(n) for n = 0..995</a>
%H A123522 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12, -21, 10).
%F A123522 a(n) = 10^n + n - 1.
%F A123522 From _Reinhard Zumkeller_, Aug 15 2010: (Start)
%F A123522 A180160(a(n)) = n and A180160(m) <> n for m < a(n).
%F A123522 A007953(a(n)) = n; A055642(a(n)) = n + 1. (End)
%F A123522 From _R. J. Mathar_, Aug 15 2010: (Start)
%F A123522 G.f.: x*(-10+19*x) / ( (10*x-1)*(x-1)^2 ).
%F A123522 a(n) = 12*a(n-1) -21*a(n-2) +10*a(n-3). (End)
%t A123522 Table[10^n + n - 1, {n, 0, 20}]  (* _Geoffrey Critzer_, Feb 03 2012 *)
%t A123522 LinearRecurrence[{12,-21,10},{0,10,101},20] (* _Harvey P. Dale_, Jul 20 2021 *)
%o A123522 (PARI) for(n=0,30, print1(10^n + n -1, ", ")) \\ _G. C. Greubel_, Nov 30 2017
%o A123522 (Magma) [10^n + n -1: n in [0..30]]; // _G. C. Greubel_, Nov 30 2017
%K A123522 easy,nonn
%O A123522 0,2
%A A123522 _Ron R. King_, Nov 10 2006
%E A123522 a(0) and terms beyond a(9) from _Reinhard Zumkeller_, Aug 15 2010