A100403 - OEIS

%I #50 Aug 09 2024 10:32:32

%S 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 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 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 Digital root of 6^n.

%C Also the digital root of k^n for any k == 6 (mod 9). - _Timothy L. Tiffin_, Dec 02 2023

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F From _Timothy L. Tiffin_, Dec 01 2023: (Start)

%F a(n) = 9 for n >= 2.

%F G.f.: (1+5x+3x^2)/(1-x).

%F a(n) = A100401(n) for n <> 1.

%F a(n) = A010888(A000400(n)) = A010888(A001024(n)) = A010888(A009968(n)) = A010888(A009977(n)) = A010888(A009986(n)) = A010888(A159991(n)). (End)

%F E.g.f.: 9*exp(x) - 3*x - 8. - _Elmo R. Oliveira_, Aug 09 2024

%e 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 PadRight[{1, 6}, 100, 9] (* _Timothy L. Tiffin_, Dec 03 2023 *)

%o (PARI) a(n) = if( n<2, [1,6][n+1], 9); \\ _Joerg Arndt_, Dec 03 2023

%Y Cf. A000400, A001024, A009968, A009977, A009986, A010888, A100401, A159991.

%K easy,nonn,base

%O 0,2

%A _Cino Hilliard_, Dec 31 2004