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 A010689 Periodic sequence: Repeat 1, 8. 13
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the digital root of 8^n. Also the decimal expansion of 2/11 = 0.181818181818... - Cino Hilliard, Dec 31 2004 Interleaving of A000012 and A010731. - Klaus Brockhaus, Apr 02 2010 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 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). 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) a(n) = 8*(n mod 2) + (n+1) mod 2 - Paolo P. Lava, Oct 20 2006 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 *) PROG (Sage) [power_mod(8, n, 9)for n in xrange(0, 105)] # Zerinvary Lajos, Nov 27 2009 (MAGMA) &cat[ [1, 8]: n in [0..52] ]; // Klaus Brockhaus, Apr 02 2010 (MAGMA) &cat [[1, 8]^^60]; // Bruno Berselli, Mar 10 2017 (Maxima) A010689(n):=if evenp(n) then 1 else 8\$ makelist(A010689(n), n, 0, 30); /* Martin Ettl, Nov 09 2012 */ (PARI) a(n)=1; if(n%2==1, 8, 1) \\ Felix FrÃ¶hlich, Aug 11 2014 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. Sequence in context: A154460 A021554 A021059 * A070637 A070651 A266528 Adjacent sequences:  A010686 A010687 A010688 * A010690 A010691 A010692 KEYWORD nonn,cofr,cons,easy AUTHOR EXTENSIONS Definition edited and keywords cons, cofr added by Klaus Brockhaus, Apr 02 2010 STATUS approved

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)