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

0,3

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

Table of n, a(n) for n=0..38.

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

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

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 *)

Prog

(Magma) &cat[ [2^n, 3^n]: n in [0..30]]; // 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

Crossrefs

Except for initial 1, reordering of A006899.

Sequence in context: A365117 A374445 A227928 * A095260 A171572 A113234

Adjacent sequences: A098290 A098291 A098292 * A098294 A098295 A098296

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved