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A098293
Powers of 2 alternating with powers of 3.
4
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.
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 18 2004
STATUS
approved