A098293 Powers of 2 alternating with powers of 3.

1, 1, 2, 3, 4, 9, 8, 27, 16, 81, 32, 243, 64, 729, 128, 2187, 256, 6561, 512, 19683, 1024, 59049, 2048, 177147, 4096, 531441, 8192, 1594323, 16384, 4782969, 32768, 14348907, 65536, 43046721, 131072, 129140163, 262144, 387420489, 524288

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

The finite sequence [1,2,3,4,9,8,27] is used in Timaios [35b] by Platon.

References

• Luc Brisson, Le Même et l'Autre dans la Structure Ontologique du Timée de Platon, Klincksieck, Paris, 1974, p. 317.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-6).

Crossrefs

Except for initial 1, reordering of A006899.

Programs

Magma

&cat[ [2^n, 3^n]: n in [0..30]]; // Vincenzo Librandi, May 10 2015

Maple

seq(seq(k^n, k=2..3), n=0..19); # Zerinvary Lajos, Jun 29 2007

Mathematica

With[{nn=20},Riffle[2^Range[0,nn],3^Range[0,nn]]] (* Harvey P. Dale, Nov 28 2011 *)
Flatten[Table[{2^n, 3^n}, {n, 0, 20}]] (* Vincenzo Librandi, May 10 2015 *)

Python

def A098293(n): return 3**(n>>1) if n&1 else 1<<(n>>1) # Chai Wah Wu, Sep 24 2024

Formula

a(2*k) = 2^k, a(2*k+1) = 3^k, k>=0.

G.f.: (1+x-3*x^2-2*x^3)/((1-2*x^2)*(1-3*x^2)).

a(n) = ((5-(-1)^n)/2)^((2*n-1+(-1)^n)/4). - Luce ETIENNE, Dec 13 2014