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Search: id:A144211
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| A144211 |
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Decimal expansion of the convergent to x = 1/(x^(1/(x+1))-1) for x > 1. |
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+0
1
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| 3, 1, 4, 1, 0, 4, 1, 5, 2, 5, 4, 1, 0, 7, 8, 8, 5, 0, 0, 9, 4, 5, 2, 3, 1, 4, 4, 6, 7, 3, 3, 5, 1, 5, 1, 5, 9, 9, 7, 9, 8, 5, 6, 8, 5, 2, 4, 4, 5, 5, 9, 9, 4, 8, 8, 1, 9, 6, 5, 4, 6, 6, 3, 1, 4, 9, 6, 4, 2, 4, 1, 1, 3, 1, 7, 6, 4, 8, 6, 7, 1, 7, 0, 2, 8, 0, 0, 8, 9, 2, 2, 6, 1, 9, 7, 3, 3, 8, 1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also the decimal expansion of a solution to 1/(x^(1/(x+1))-1)-x.
The other solution is 1. Is the first 4 digits 3,1,4,1 a just a coincidence?
Perhaps Pi - 3.1410415254107... = 0.0005511281790... has a generating function.
Some experimentation will show that the recurrence
x = 1/(x^(1/(x+1))-1-1/x^8.446) converges to 3.14159264313...
Apparently related to A100086. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
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PROGRAM
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(PARI) y=solve(x=3, 4, 1/(x^(1/(x+1))-1)-x); a=eval(Vec(Str(y*10^99)));
for(j=1, 99, print1(a[j]", "))
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CROSSREFS
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Sequence in context: A021765 A051512 A079668 this_sequence A125291 A055187 A109411
Adjacent sequences: A144208 A144209 A144210 this_sequence A144212 A144213 A144214
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KEYWORD
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base,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Sep 14 2008
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