A007450 Decimal expansion of 1/17. (Formerly M3772)

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

0,2

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

Ross Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 148.

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).

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

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 *)

Prog

(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
(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 */

Crossrefs

Cf. A002371, A028416, A049084.

Sequence in context: A259234 A131040 A231786 * A303816 A342647 A200297

Adjacent sequences: A007447 A007448 A007449 * A007451 A007452 A007453

Keyword

cons,nonn,easy

Author

N. J. A. Sloane

Status

approved