

A078886


Decimal expansion of Sum {n=0..inf} 1/5^(2^n).


9



2, 4, 1, 6, 0, 2, 5, 6, 0, 0, 0, 6, 5, 5, 3, 6, 0, 0, 0, 0, 0, 0, 4, 2, 9, 4, 9, 6, 7, 2, 9, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 4, 4, 6, 7, 4, 4, 0, 7, 3, 7, 0, 9, 5, 5, 1, 6, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 2, 8, 2, 3, 6, 6, 9, 2, 0, 9, 3, 8, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Sum {0..infinity} 1/5^(2^n) = 0.241602560006553600000...
Decimal expansion has increasingly large gaps of zeros, the digits delimited by these zeros are equal to 2^(2^m) as m=0,1,2,3,... The continued fraction expansion (A122165) and consists entirely of 3's, 5's and 7's, after an initial partial quotient of 4.  Paul D. Hanna, Aug 22 2006


LINKS

Table of n, a(n) for n=0..104.


EXAMPLE

Decimal expansion consists of large gaps of zeros between strings of digits that form powers of 2; this can be seen by grouping the digits as follows:
x = .2 4 16 0 256 000 65536 000000 4294967296 000000000000 ...= 0.24160256000655360000004294...
and then recognizing the substrings as powers of 2:
2 = 2^(2^0), 4 = 2^(2^1), 16 = 2^(2^2), 65536 = 2^(2^4), 4294967296 = 2^(2^5), 18446744073709551616 = 2^(2^6), ...  Paul D. Hanna, Aug 22 2006


MATHEMATICA

RealDigits[ N[ Sum[1/5^(2^n), {n, 0, Infinity}], 110]][[1]]


PROG

(PARI) {a(n)=local(x=sum(k=0, ceil(3+log(n+1)), 1/5^(2^k))); (floor(10^n*x))%10}  Paul D. Hanna, Aug 22 2006


CROSSREFS

Cf. A007404, A078885, A078585, A078887, A078888, A078889, A078890, A036987.
Cf. A122165.
Sequence in context: A286784 A047908 A125847 * A307796 A095247 A007734
Adjacent sequences: A078883 A078884 A078885 * A078887 A078888 A078889


KEYWORD

cons,nonn


AUTHOR

Robert G. Wilson v, Dec 11 2002


EXTENSIONS

Edited by R. J. Mathar, Aug 02 2008


STATUS

approved



