This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A283526 #32 Nov 21 2024 21:26:32
%S A283526 1,2,3,4,5,16,17,256,257,65536,65537,4294967296,4294967297,
%T A283526 18446744073709551616,18446744073709551617,
%U A283526 340282366920938463463374607431768211456,340282366920938463463374607431768211457
%N A283526 Pierce expansion of the number Sum_{k >= 1} 1/(2^(2^k - 1)).
%C A283526 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 A283526 Michael De Vlieger, <a href="/A283526/b283526.txt">Table of n, a(n) for n = 0..24</a>
%H A283526 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 A283526 a(0) = 1, a(2k+1) = 2^(2^k), a(2k+2) = 2^(2^k) + 1.
%e A283526 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 A283526 L:=[1]: for k from 0 to 6 do: L:=[op(L),2^(2^k),2^(2^k)+1]: od: print(L);
%t A283526 {1}~Join~Map[{#, # + 1} &, 2^2^Range[0, 8]] // Flatten (* _Michael De Vlieger_, Mar 18 2017 *)
%Y A283526 Cf. A006466, A007400, A076214.
%K A283526 nonn
%O A283526 0,2
%A A283526 _Kutlwano Loeto_, Mar 10 2017