A283526 Pierce expansion of the number Sum_{k >= 1} 1/(2^(2^k - 1)).

1, 2, 3, 4, 5, 16, 17, 256, 257, 65536, 65537, 4294967296, 4294967297, 18446744073709551616, 18446744073709551617, 340282366920938463463374607431768211456, 340282366920938463463374607431768211457

Offset

0,2

Comments

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.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..24

Jeffrey Shallit, Simple continued fractions for some irrational numbers. J. Number Theory 11 (1979), no. 2, 209-217.

Formula

a(0) = 1, a(2k+1) = 2^(2^k), a(2k+2) = 2^(2^k) + 1.

Example

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) + ...

Maple

L:=[1]: for k from 0 to 6 do: L:=[op(L), 2^(2^k), 2^(2^k)+1]: od: print(L);

Mathematica

{1}~Join~Map[{#, # + 1} &, 2^2^Range[0, 8]] // Flatten (* Michael De Vlieger, Mar 18 2017 *)

Crossrefs

Cf. A006466, A007400, A076214.

Sequence in context: A177334 A004834 A075687 * A293824 A095181 A240906

Adjacent sequences: A283523 A283524 A283525 * A283527 A283528 A283529

Keyword

nonn

Author

Kutlwano Loeto, Mar 10 2017

Status

approved