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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 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 May 21 08:48 EDT 2019. Contains 323441 sequences. (Running on oeis4.)