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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

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Last modified November 12 19:41 EST 2019. Contains 329078 sequences. (Running on oeis4.)