A007450 Decimal expansion of 1/17.

0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7, 0, 5, 8, 8, 2, 3, 5

Offset: 0

Author

N. J. A. Sloane

Keywords

• cons
• nonn
• easy

Comments

Period 16: repeat [0, 5, 8, 8, 2, 3, 5, 2, 9, 4, 1, 1, 7, 6, 4, 7]. - Joerg Arndt, Mar 25 2013

References

• H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'. [From Reinhard Zumkeller, Oct 06 2008]
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• R. K. Hoeflin, Mega Test
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).

Programs

Magma

I:=[0, 5, 8, 8, 2, 3, 5, 2, 9]; [n le 9 select I[n] else Self(n-1)-Self(n-8)+Self(n-9): n in [1..100]]; // Vincenzo Librandi, Mar 25 2013

Mathematica

CoefficientList[Series[-x (7 x^7 - 3 x^6 + 2 x^5 + x^4 - 6 x^3 + 3 x + 5)/((x - 1) (x^8+1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 25 2013 *)

PARI

a(n)=[0,5,8,8,2,3,5,2,9,4,1,1,7,6,4,7][n%16+1]; /* Joerg Arndt, Mar 25 2013 */

Formula

From Reinhard Zumkeller, Oct 06 2008: (Start)

A028416(4)=17; A002371(A049084(17)) = A002371(7)=16;

a(n+16) = a(n), a(n+16/2) = 9 - a(n). (End)

G.f.: -x*(7*x^7-3*x^6+2*x^5+x^4-6*x^3+3*x+5)/((x-1)*(x^8+1)). - Colin Barker, Aug 15 2012