A010689 Periodic sequence: Repeat 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, 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, 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
Offset: 0
Examples
0.18181818181818181818181818181818181818181...
References
- Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.
Links
- Index entries for linear recurrences with constant coefficients, signature (0,1).
Crossrefs
Cf. A000012 (all 1's sequence), A010731 (all 8's sequence), A174925 (decimal expansion of (2 + sqrt(6))/4). [Klaus Brockhaus, Apr 02 2010]
Cf. Digital roots of powers of c mod 9: c = 2, A153130; c = 4, A100402; c = 5, A070366; c = 7, A070403.
Cf. sequences listed in Comments section of A283393.
Cf. A010888.
Programs
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Magma
&cat[ [1, 8]: n in [0..52] ]; // Klaus Brockhaus, Apr 02 2010
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Magma
&cat [[1,8]^^60]; // Bruno Berselli, Mar 10 2017
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Mathematica
Table[Mod[8^n, 9], {n, 0, 99}] (* Alonso del Arte, Jan 26 2014 *) PadRight[{},120,{1,8}] (* Harvey P. Dale, Jun 03 2015 *) -
Maxima
A010689(n):=if evenp(n) then 1 else 8$ makelist(A010689(n),n,0,30); /* Martin Ettl, Nov 09 2012 */
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PARI
a(n)=1; if(n%2==1, 8, 1) \\ Felix Fröhlich, Aug 11 2014
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Sage
[power_mod(8,n,9)for n in range(0,105)] # Zerinvary Lajos, Nov 27 2009
Formula
From Paul Barry, Sep 16 2004: (Start)
G.f.: (1 + 8*x)/((1 - x)*(1 + x)).
a(n) = (9 - 7*(-1)^n)/2.
a(n) = 8^(ceiling(n/2) - floor(n/2)).
a(n) = gcd((n-1)^3, (n+1)^3). (End)
E.g.f.: cosh(x) + 8*sinh(x). - Stefano Spezia, Feb 09 2025
a(n) = A010888(8*a(n-1)). - Stefano Spezia, Mar 20 2025
Extensions
Definition edited and keywords cons, cofr added by Klaus Brockhaus, Apr 02 2010
Comments