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A010689
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Periodic sequence: Repeat 1, 8.
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14
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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
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OFFSET
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0,2
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COMMENTS
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Also the digital root of 8^n. Also the decimal expansion of 2/11 = 0.181818181818... - Cino Hilliard, Dec 31 2004
Continued fraction expansion of (2 + sqrt(6))/4. - Klaus Brockhaus, Apr 02 2010
Digital root of the powers of any number congruent to 8 mod 9. - Alonso del Arte, Jan 26 2014
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REFERENCES
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Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.
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LINKS
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FORMULA
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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)
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MATHEMATICA
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PROG
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(Sage) [power_mod(8, n, 9)for n in range(0, 105)] # Zerinvary Lajos, Nov 27 2009
(Maxima) A010689(n):=if evenp(n) then 1 else 8$
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CROSSREFS
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Cf. sequences listed in Comments section of A283393.
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KEYWORD
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AUTHOR
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EXTENSIONS
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Definition edited and keywords cons, cofr added by Klaus Brockhaus, Apr 02 2010
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STATUS
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approved
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