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 A218721 #54 Mar 13 2023 06:52:45
%S A218721 0,1,19,343,6175,111151,2000719,36012943,648232975,11668193551,
%T A218721 210027483919,3780494710543,68048904789775,1224880286215951,
%U A218721 22047845151887119,396861212733968143,7143501829211426575,128583032925805678351
%N A218721 a(n) = (18^n-1)/17.
%C A218721 Partial sums of powers of 18 (A001027), q-integers for q=18: diagonal k=1 in triangle A022182.
%C A218721 Partial sums are in A014901. Also, the sequence is related to A014935 by A014935(n) = n*a(n) - Sum_{i=0..n-1} a(i), for n>0. - _Bruno Berselli_, Nov 06 2012
%C A218721 From _Bernard Schott_, May 06 2017: (Start)
%C A218721 Except for 0, 1 and 19, all terms are Brazilian repunits numbers in base 18, and so belong to A125134. From n = 3 to n = 8286, all terms are composite. See link "Generalized repunit primes".
%C A218721 As explained in the extensions of A128164, a(25667) = (18^25667 - 1)/17 would be (is) the smallest prime in base 18. (End)
%H A218721 Vincenzo Librandi, <a href="/A218721/b218721.txt">Table of n, a(n) for n = 0..800</a>
%H A218721 Harvey Dubner, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1185243-9">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930.
%H A218721 <a href="/index/Par#partial">Index entries related to partial sums</a>
%H A218721 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (19,-18).
%F A218721 a(n) = floor(18^n/17).
%F A218721 G.f.: x/((1-x)*(1-18*x)). - _Bruno Berselli_, Nov 06 2012
%F A218721 a(n) = 19*a(n-1) - 18*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%F A218721 E.g.f.: exp(x)*(exp(17*x) - 1)/17. - _Stefano Spezia_, Mar 11 2023
%e A218721 a(3) = (18^3 - 1)/17 = 343 = 7 * 49; a(6) = (18^6 - 1)/17 = 2000719 = 931 * 2149. - _Bernard Schott_, May 01 2017
%t A218721 LinearRecurrence[{19, -18}, {0, 1}, 40] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218721 Join[{0},Accumulate[18^Range[0,20]]] (* _Harvey P. Dale_, Nov 08 2012 *)
%o A218721 (PARI) A218721(n)=18^n\17
%o A218721 (Maxima) A218721(n):=(18^n-1)/17$ makelist(A218721(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A218721 (Magma) [n le 2 select n-1 else 19*Self(n-1)-18*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%Y A218721 Cf. A000225, A001027, A002275, A002450, A002452, A003462, A003463, A003464, A014901, A014935, A016123, A016125, A022182, A023000, A023001, A064108, A091030, A091045, A094028, A125134, A128164, A131865, A135518, A135519, A218722, A218724, A218733, A218743, A218752.
%K A218721 nonn,easy
%O A218721 0,3
%A A218721 _M. F. Hasler_, Nov 04 2012