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

0,2

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

Table of n, a(n) for n=0..99.

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A154180 A011332 A092235 * A242908 A023578 A111487

Adjacent sequences: A130791 A130792 A130793 * A130795 A130796 A130797

Keyword

nonn,easy,less

Author

Paul Curtz, Jul 15 2007

Status

approved