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A144211
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Decimal expansion of solution to (x+1)^(x+1) = x^(x+2).
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Decimal expansion of the convergent to x = 1/(x^(1/(x+1))-1) for x > 1.
Also the decimal expansion of a solution to 1/(x^(1/(x+1))-1)-x. The other solution is 1.
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...
Equals A100086 minus 1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 25 2010]
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EXAMPLE
| 3.141041525410788500945231446733515159979856852445599488196546631496424\
113176486717028008922619733816396791510643825934571540309860365903143378\
733054296284455377...
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PROG
| (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
| Sequence in context: A021765 A051512 A079668 * A125291 A055187 A109411
Adjacent sequences: A144208 A144209 A144210 * A144212 A144213 A144214
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KEYWORD
| base,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Sep 14 2008
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EXTENSIONS
| Made comment more precise - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 25 2010
Edited by N. J. A. Sloane, Jul 05 2010
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