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 A186830 #21 Feb 16 2025 08:33:14
%S A186830 1,9,7,17,33,57,107,197,361,665,1223,2249,4137,7609,13995,25741,47345,
%T A186830 87081,160167,294593,541841,996601,1833035,3371477,6201113,11405625,
%U A186830 20978215,38584953,70968793,130531961
%N A186830 Keith sequence for the number 197.
%C A186830 This sequence illustrates why 197 is a Keith number (cf. A007629).
%C A186830 Other multiples of 197 in the sequence are 4137 and 992207243244533. - _Alonso del Arte_, Mar 14 2011
%H A186830 M. Klazar and F. Luca, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Klazar/klazar15.html">Counting Keith numbers</a>, Journal of Integer Sequences, Vol. 10 (2007), #07.2.2.
%H A186830 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KeithNumber.html">Keith Number</a>
%H A186830 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A186830 a(1)=1, a(2)=9, a(3)=7; thereafter a(n) = sum of previous three terms. Note that 197 appears in the sequence, which is why 197 is a Keith number.
%F A186830 G.f.: x*(1+8*x-3*x^2)/(1-x-x^2-x^3). [_Colin Barker_, Jun 19 2012]
%t A186830 keithSeq[n_Integer, b_:10, goBeyondN_:0] := Module[{seq = IntegerDigits[n, b], ord, max = n + goBeyondN, curr}, ord = Length[seq]; curr = seq[[-1]]; While[curr < max, curr = Plus@@Take[seq, -ord]; seq = Append[seq, curr]]; Return[seq]]; keithSeq[197, 10, 10^8] (* _Alonso del Arte_, Mar 14 2011 *)
%o A186830 (PARI) Vec((1+8*x-3*x^2)/(1-x-x^2-x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Feb 04 2013
%Y A186830 Cf. A007629.
%K A186830 nonn,base,easy
%O A186830 1,2
%A A186830 _N. J. A. Sloane_, Feb 27 2011