A010703 Period 2: repeat (3,5).

3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

From Klaus Brockhaus, Dec 10 2009: (Start)

Interleaving of A010701 and A010716.

Also continued fraction expansion of (15+sqrt(285))/10.

Also decimal expansion of 35/99.

Binomial transform of 3 followed by A084633 without initial terms 1,0.

Inverse binomial transform of A171497. (End)

Links

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

Crossrefs

Cf. A010701 (all 3's sequence), A010716 (all 5's sequence), A084633 (inverse binomial transform of repeated odd numbers), A171497.

Programs

Magma

&cat[ [3, 5]: n in [1..53] ]; // Klaus Brockhaus, Dec 10 2009

Mathematica

Table[If[OddQ[n], 3, 5], {n, 1, 50}] (* Stefan Steinerberger, Apr 10 2006 *)
PadRight[{},120,{3,5}] (* Harvey P. Dale, Sep 03 2012 *)

PARI

a(n)=3+n%2*2 \\ Charles R Greathouse IV, Nov 20 2011

Formula

From Klaus Brockhaus, Dec 10 2009: (Start)

a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = 5.

G.f.: (3+5*x)/((1-x)*(1+x)). (End)

a(n) = 4 - (-1)^n. - Aaron J Grech, Aug 02 2024

E.g.f.: 3*cosh(x) + 5*sinh(x). - Stefano Spezia, Aug 04 2024