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Search: id:A122165
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| A122165 |
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Continued fraction expansion of constant x = Sum_{n>=0} 1/5^(2^n). |
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+0
2
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| 0, 4, 7, 5, 5, 3, 5, 7, 5, 3, 7, 5, 3, 5, 5, 7, 5, 3, 7, 5, 5, 3, 5, 7, 3, 5, 7, 5, 3, 5, 5, 7, 5, 3, 7, 5, 5, 3, 5, 7, 5, 3, 7, 5, 3, 5, 5, 7, 3, 5, 7, 5, 5, 3, 5, 7, 3, 5, 7, 5, 3, 5, 5, 7, 5, 3, 7, 5, 5, 3, 5, 7, 5, 3, 7, 5, 3, 5, 5, 7, 5, 3, 7, 5, 5, 3, 5, 7, 3, 5, 7, 5, 3, 5, 5, 7, 3, 5, 7, 5, 5, 3, 5, 7, 5
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Consists entirely of 3's, 5's and 7's, after an initial partial quotient of 4. These partial quotients are aperiodic.
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EXAMPLE
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x=[0;4,7,5,5,3,5,7,5,3,7,5,3,5,5,7,5,3,7,5,5,3,5,7,3,5,7,5,3,5,5,7,5,...].
x=0.2416025600065536000000429496729600000000000018446744073709551616000...
Decimal expansion (A078886) 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), ...
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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))); contfrac(x)[n+1]}
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CROSSREFS
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Cf. A078886.
Sequence in context: A132265 A079356 A146539 this_sequence A086202 A107824 A085674
Adjacent sequences: A122162 A122163 A122164 this_sequence A122166 A122167 A122168
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KEYWORD
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cofr,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 22 2006
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