A098293 - OEIS

%I #31 Sep 25 2024 01:47:59

%S 1,1,2,3,4,9,8,27,16,81,32,243,64,729,128,2187,256,6561,512,19683,

%T 1024,59049,2048,177147,4096,531441,8192,1594323,16384,4782969,32768,

%U 14348907,65536,43046721,131072,129140163,262144,387420489,524288

%N Powers of 2 alternating with powers of 3.

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

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-6).

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

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

%F a(n) = ((5-(-1)^n)/2)^((2*n-1+(-1)^n)/4). - _Luce ETIENNE_, Dec 13 2014

%p seq(seq(k^n, k=2..3), n=0..19); # _Zerinvary Lajos_, Jun 29 2007

%t With[{nn=20},Riffle[2^Range[0,nn],3^Range[0,nn]]] (* _Harvey P. Dale_, Nov 28 2011 *)

%t Flatten[Table[{2^n, 3^n}, {n, 0, 20}]] (* _Vincenzo Librandi_, May 10 2015 *)

%o (Magma) &cat[ [2^n, 3^n]: n in [0..30]]; // _Vincenzo Librandi_, May 10 2015

%o (Python)

%o def A098293(n): return 3**(n>>1) if n&1 else 1<<(n>>1) # _Chai Wah Wu_, Sep 24 2024

%Y Except for initial 1, reordering of A006899.

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 18 2004