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Search: id:A078886
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| A078886 |
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Decimal expansion of Sum {n=0..inf} 1/5^(2^n). |
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+0
10
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| 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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (pauldhanna(AT)juno.com), Aug 22 2006
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EXAMPLE
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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 ...
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 (pauldhanna(AT)juno.com), Aug 22 2006
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MATHEMATICA
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RealDigits[ N[ Sum[1/5^(2^n), {n, 0, Infinity}], 110]][[1]]
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PROGRAM
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(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 (pauldhanna(AT)juno.com), Aug 22 2006
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CROSSREFS
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Cf. A007404, A078885, A078585, A078887, A078888, A078889, A078890, A036987.
Cf. A122165.
Adjacent sequences: A078883 A078884 A078885 this_sequence A078887 A078888 A078889
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KEYWORD
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cons,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 11 2002
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2008
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