A130794 Periodic sequence with period 1,5,3.

1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1, 5, 3, 1

Offset: 0

Author

Paul Curtz, Jul 15 2007

Keywords

• nonn
• easy
• less

Comments

Continued fraction expansion of (7+sqrt(145))/16. - Klaus Brockhaus, Apr 28 2010

Decimal expansion of 17/111. - R. J. Mathar, Aug 05 2013

This is also the periodic unsigned Schick sequence for 7. See the Schick reference, p. 158 for p = 7 (the row labels should there be q_j, j >= 0). - Wolfdieter Lang, Apr 03 2020

References

• Carl Schick, Trigonometrie und unterhaltsame Zahlentheorie, Bokos Druck, Zürich, 2003 (ISBN 3-9522917-0-6). Tables 3.1 to 3.10, for odd p = 3..113 (with gaps), pp. 158-166. Here p = 7.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A176908 (decimal expansion of (7+sqrt(145))/16). - Klaus Brockhaus, Apr 28 2010

Programs

Maple

A130794:=n->5 - 2 * ((n+2) mod 3); seq(A130794(n), n=0..100); # Wesley Ivan Hurt, Mar 15 2014

Mathematica

Table[5 - 2 Mod[n + 2, 3], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 15 2014 *)
PadRight[{},120,{1,5,3}] (* Harvey P. Dale, Jun 15 2019 *)

PARI

a(n)=[1,5,3][n%3+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

G.f.: ( -1-5*x-3*x^2 ) / ( (x-1)*(1+x+x^2) ). - R. J. Mathar, Aug 05 2013

a(n) = 5 - 2 * mod(n+2,3). - Wesley Ivan Hurt, Mar 15 2014