|
%I #29 Mar 26 2017 14:40:07
%S 1,2,3,4,5,16,17,256,257,65536,65537,4294967296,4294967297,
%T 18446744073709551616,18446744073709551617,
%U 340282366920938463463374607431768211456,340282366920938463463374607431768211457
%N Pierce expansion of the number Sum_{k >= 1} 1/(2^(2^k - 1)).
%C This sequence is the Pierce expansion of the number 2*s(2) - 1 = 0.632843018043786287416159475061... where s(u) = Sum_{k>=0) 1/u^(2^k) that has been considered by J. Shallit in A007400. The continued fraction expansion of this number is essentially A006466.
%H Michael De Vlieger, <a href="/A283526/b283526.txt">Table of n, a(n) for n = 0..24</a>
%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) = 1, a(2k+1) = 2^(2^k), a(2k+2) = 2^(2^k) + 1.
%e The Pierce expansion of 0.6328430180437862 starts as 1 - 1/2 + 1/(2*3) - 1/(2*3*4) + 1/(2*3*4*5) - 1/(2*3*4*5*16) + ...
%p L:=[1]: for k from 0 to 6 do: L:=[op(L),2^(2^k),2^(2^k)+1]: od: print(L);
%t {1}~Join~Map[{#, # + 1} &, 2^2^Range[0, 8]] // Flatten (* _Michael De Vlieger_, Mar 18 2017 *)
%Y Cf. A006466, A007400, A076214.
%K nonn
%O 0,2
%A _Kutlwano Loeto_, Mar 10 2017
| 