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 A010689 #58 Mar 20 2025 09:10:19
%S A010689 1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,
%T A010689 1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,
%U A010689 1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1
%N A010689 Periodic sequence: Repeat 1, 8.
%C A010689 Also the digital root of 8^n. Also the decimal expansion of 2/11 = 0.181818181818... - _Cino Hilliard_, Dec 31 2004
%C A010689 Interleaving of A000012 and A010731. - _Klaus Brockhaus_, Apr 02 2010
%C A010689 Continued fraction expansion of (2 + sqrt(6))/4. - _Klaus Brockhaus_, Apr 02 2010
%C A010689 Digital root of the powers of any number congruent to 8 mod 9. - _Alonso del Arte_, Jan 26 2014
%D A010689 Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.
%H A010689 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A010689 From _Paul Barry_, Sep 16 2004: (Start)
%F A010689 G.f.: (1 + 8*x)/((1 - x)*(1 + x)).
%F A010689 a(n) = (9 - 7*(-1)^n)/2.
%F A010689 a(n) = 8^(ceiling(n/2) - floor(n/2)).
%F A010689 a(n) = gcd((n-1)^3, (n+1)^3). (End)
%F A010689 E.g.f.: cosh(x) + 8*sinh(x). - _Stefano Spezia_, Feb 09 2025
%F A010689 a(n) = A010888(8*a(n-1)). - _Stefano Spezia_, Mar 20 2025
%e A010689 0.18181818181818181818181818181818181818181...
%t A010689 Table[Mod[8^n, 9], {n, 0, 99}] (* _Alonso del Arte_, Jan 26 2014 *)
%t A010689 PadRight[{},120,{1,8}] (* _Harvey P. Dale_, Jun 03 2015 *)
%o A010689 (Sage) [power_mod(8,n,9)for n in range(0,105)] # _Zerinvary Lajos_, Nov 27 2009
%o A010689 (Magma) &cat[ [1, 8]: n in [0..52] ]; // _Klaus Brockhaus_, Apr 02 2010
%o A010689 (Magma) &cat [[1,8]^^60]; // _Bruno Berselli_, Mar 10 2017
%o A010689 (Maxima) A010689(n):=if evenp(n) then 1 else 8$
%o A010689 makelist(A010689(n),n,0,30); /* _Martin Ettl_, Nov 09 2012 */
%o A010689 (PARI) a(n)=1; if(n%2==1, 8, 1) \\ _Felix Fröhlich_, Aug 11 2014
%Y A010689 Cf. A000012 (all 1's sequence), A010731 (all 8's sequence), A174925 (decimal expansion of (2 + sqrt(6))/4). [_Klaus Brockhaus_, Apr 02 2010]
%Y A010689 Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 4, A100402; c = 5, A070366; c = 7, A070403.
%Y A010689 Cf. sequences listed in Comments section of A283393.
%Y A010689 Cf. A010888.
%K A010689 nonn,cofr,cons,easy
%O A010689 0,2
%A A010689 _N. J. A. Sloane_
%E A010689 Definition edited and keywords cons, cofr added by _Klaus Brockhaus_, Apr 02 2010