cp's OEIS Frontend

A070403 a(n) = 7^n mod 9.

%I A070403 #56 Mar 20 2025 09:43:39
%S A070403 1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,
%T A070403 7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,
%U A070403 4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4,1,7,4
%N A070403 a(n) = 7^n mod 9.
%C A070403 Also the digital root of 7^n. If we convert this to a repeating decimal 0.174174..., we get the rational number 58/333. - _Cino Hilliard_, Dec 31 2004
%C A070403 A141722 (1, 25, 121, 505, 2041, 8185) mod 9. Note A141722 = 10*A000975(2n) + A000975(2n+1). - _Paul Curtz_, Sep 15 2008
%C A070403 Digital root of the powers of any number congruent to 7 mod 9. - _Alonso del Arte_, Jan 26 2014
%D A070403 Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.
%H A070403 Vincenzo Librandi, <a href="/A070403/b070403.txt">Table of n, a(n) for n = 0..1000</a>
%H A070403 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1).
%F A070403 From _R. J. Mathar_, Feb 23 2009: (Start)
%F A070403 G.f.: (1+7*x+4*x^2)/((1-x)*(1+x+x^2)).
%F A070403 a(n+1) - a(n) = 3*A099837(n+3).
%F A070403 a(n) = 4 - 3*A049347(n). (End)
%F A070403 a(n) = a(n-3) for n>3. - _G. C. Greubel_, Mar 19 2016
%F A070403 a(n) = 4-2*sqrt(3)*sin((2*n+2)*Pi/3). - _Wesley Ivan Hurt_, Jun 09 2016
%F A070403 a(n) = A010888(7*a(n-1)). - _Stefano Spezia_, Mar 20 2025
%p A070403 A070403:=n->4-2*sqrt(3)*sin(2*(n+1)*Pi/3): seq(A070403(n), n=0..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t A070403 Table[PowerMod[7, n, 9], {n, 0, 200}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 10 2011 *)
%o A070403 (Sage) [power_mod(7,n,9)for n in range(0,105)] # _Zerinvary Lajos_, Nov 03 2009
%o A070403 (PARI) a(n)=7^n%9 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A070403 (Magma) [Modexp(7, n, 9): n in [0..110]]; // _Bruno Berselli_, Mar 22 2016
%Y A070403 Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 4, A100402; c = 5, A070366; c = 8, A010689.
%Y A070403 Cf. A000975, A010888, A049347, A099837, A141722.
%K A070403 nonn,easy
%O A070403 0,2
%A A070403 _N. J. A. Sloane_, May 12 2002