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

0,2

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

Table of n, a(n) for n=0..104.

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)

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 range(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 Fröhlich, 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

N. J. A. Sloane

Extensions

Definition edited and keywords cons, cofr added by Klaus Brockhaus, Apr 02 2010

Status

approved