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 A100403 #55 Mar 20 2025 08:40:02
%S A100403 1,6,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%T A100403 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U A100403 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A100403 Digital root of 6^n.
%C A100403 Also the digital root of k^n for any k == 6 (mod 9). - _Timothy L. Tiffin_, Dec 02 2023
%H A100403 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A100403 From _Timothy L. Tiffin_, Dec 01 2023: (Start)
%F A100403 a(n) = 9 for n >= 2.
%F A100403 G.f.: (1+5x+3x^2)/(1-x).
%F A100403 a(n) = A100401(n) for n <> 1.
%F A100403 a(n) = A010888(A000400(n)) = A010888(A001024(n)) = A010888(A009968(n)) = A010888(A009977(n)) = A010888(A009986(n)) = A010888(A159991(n)). (End)
%F A100403 E.g.f.: 9*exp(x) - 3*x - 8. - _Elmo R. Oliveira_, Aug 09 2024
%F A100403 a(n) = A007953(6*a(n-1)) = A010888(6*a(n-1)). - _Stefano Spezia_, Mar 20 2025
%e A100403 For n=8, the digits of 6^8 = 1679616 sum to 36, whose digits sum to 9. So, a(8) = 9. - _Timothy L. Tiffin_, Dec 01 2023
%t A100403 PadRight[{1, 6}, 100, 9] (* _Timothy L. Tiffin_, Dec 03 2023 *)
%o A100403 (PARI) a(n) = if( n<2, [1,6][n+1], 9); \\ _Joerg Arndt_, Dec 03 2023
%Y A100403 Cf. A000400, A001024, A007953, A009968, A009977, A009986, A010888, A100401, A159991.
%K A100403 easy,nonn,base
%O A100403 0,2
%A A100403 _Cino Hilliard_, Dec 31 2004