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%I #51 Sep 09 2017 03:32:37
%S 2,3,4,9,10,81,82,6561,6562,43046721,43046722,1853020188851841,
%T 1853020188851842,3433683820292512484657849089281,
%U 3433683820292512484657849089282,11790184577738583171520872861412518665678211592275841109096961,11790184577738583171520872861412518665678211592275841109096962
%N The Pierce expansion of the number Sum_{k>=1} 1/3^((2^k) - 1).
%C This sequence is the Pierce expansion of the number 3*s(3) - 1 = 0.370827687432918983346475478500709113969827799141493576... where s(u) = Sum_{k>=0) 1/u^(2^k) for u=3 has been considered by _N. J. A. Sloane_ in A004200.
%C The continued fraction expansion of the number 3*s(3)-1 is essentially A081771.
%H Jeffrey Shallit, <a href="http://dx.doi.org/10.1016/0022-314X(79)90040-4">Simple continued fractions for some irrational numbers</a>. J. Number Theory 11 (1979), no. 2, 209-217.
%F a(0) = 2, a(2k+1) = 3^(2^k), a(2k+2) = 3^(2^k) + 1, k >= 0.
%e The Pierce expansion of 0.3708276874329189833 starts as 1/2 - 1/(2*3) + 1/(2*3*4) - 1/(2*3*4*9) + 1/(2*3*4*9*10) - 1/(2*3*4*9*10*81) + ...
%p L:=[2]: for k from 0 to 6 do: L:=[op(L),3^(2^k),3^(2^k)+1]: od: print(L);
%o (PARI) a(n) = if (n==0, 2, if (n%2, 3^(2^((n-1)/2)), 3^(2^((n-2)/2))+1)); \\ _Michel Marcus_, Mar 31 2017
%K nonn
%O 0,1
%A _Kutlwano Loeto_, Mar 24 2017
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