

A051158


Decimal expansion of Sum_{n >= 0} 1/(2^2^n+1).


3



5, 9, 6, 0, 6, 3, 1, 7, 2, 1, 1, 7, 8, 2, 1, 6, 7, 9, 4, 2, 3, 7, 9, 3, 9, 2, 5, 8, 6, 2, 7, 9, 0, 6, 4, 5, 4, 6, 2, 3, 6, 1, 2, 3, 8, 4, 7, 8, 1, 0, 9, 9, 3, 2, 6, 2, 1, 4, 4, 2, 4, 5, 9, 9, 6, 0, 9, 1, 0, 8, 9, 9, 7, 7, 4, 8, 8, 6, 0, 8, 8, 8, 9, 9, 3, 6, 1, 9, 1, 8, 4, 6, 4, 6, 4, 4, 0, 7, 4
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OFFSET

0,1


LINKS

Table of n, a(n) for n=0..98.
Joerg Arndt: Matters Computational (The Fxtbook), section 38.7, p.740 (gives method for divisionless computation corresponding to pari/gp code below).
M. Coons, On the rational approximation of the sum of the reciprocals of the Fermat numbers, Raman. J. 28 (2012)
Michael Coons, Addendum to: On the rational approximation of the sum of the reciprocals of the Fermat numbers, arXiv:1511.08147 [math.NT], 2015.
S. W. Golomb, On the sum of the reciprocals of the Fermat numbers and related irrationalities, Canad. J. Math., 15 (1963), 475478.


EXAMPLE

.59606317211782167942...


MATHEMATICA

RealDigits[Sum[1/(2^2^n + 1), {n, 0, 10}], 10, 111][[1]] (* Robert G. Wilson v, Jul 03 2014 *)


PROG

(PARI) /* divisionless routine from fxtbook */
s2(y, N=7)=
{ local(in, y2, A); /* as powerseries correct to order = 2^N1 */
in = 1; /* 1+y+y^2+y^3+...+y^(2^k1) */
A = y; for(k=2, N, in *= (1+y); y *= y; A += y*(in + A); );
return( A ); }
a=0.5*s2(0.5) /* computation of the constant 0.596063172117821... */
/* Joerg Arndt, Apr 15 2010 */


CROSSREFS

A048649 + A051158 = 2.
Terms in continued fraction: A159243. [Enrique Pérez Herrero, Nov 17 2009]
Sequence in context: A057821 A133742 A134879 * A117605 A073003 A087498
Adjacent sequences: A051155 A051156 A051157 * A051159 A051160 A051161


KEYWORD

nonn,cons,changed


AUTHOR

Robert Lozyniak (11(AT)onna.com)


STATUS

approved



