A100941 Decimal expansion of the nested surd sqrt(Pi + sqrt(Pi + sqrt(Pi + ...))).
2, 3, 4, 1, 6, 2, 7, 7, 1, 8, 5, 1, 1, 4, 7, 8, 4, 3, 1, 7, 6, 6, 5, 8, 6, 0, 6, 2, 2, 9, 6, 9, 5, 5, 6, 7, 8, 7, 1, 2, 6, 0, 8, 5, 4, 7, 7, 4, 4, 0, 1, 9, 0, 1, 3, 6, 1, 5, 4, 5, 7, 3, 8, 1, 7, 6, 8, 8, 6, 3, 5, 0, 9, 1, 2, 8, 7, 0, 7, 8, 0, 4, 6, 6, 8, 6, 4, 0, 8, 5, 5, 5, 1, 8, 5, 8, 8, 7, 5, 5
Offset: 1
Examples
2.34162771851147843176658606229695567871260854774401...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
Crossrefs
Cf. A100942 for continued fraction.
Programs
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Mathematica
RealDigits[(1+Sqrt[1+4Pi])/2,10,120][[1]] (* Harvey P. Dale, Dec 04 2014 *)
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PARI
default(realprecision,100); t=0; for(n=1,5000,t=sqrt(t+Pi)); t
Formula
This is the solution of the quadratic equation y^2-y-Pi=0.