A100941 - OEIS

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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

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OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

This is the solution of the quadratic equation y^2-y-Pi=0.

EXAMPLE

2.34162771851147843176658606229695567871260854774401...

MATHEMATICA

RealDigits[(1+Sqrt[1+4Pi])/2, 10, 120][[1]] (* Harvey P. Dale, Dec 04 2014 *)

PROG

(PARI) default(realprecision, 100):t=0:for(n=1, 5000, t=sqrt(t+Pi)):return(t)

CROSSREFS

Cf. A100942 for continued fraction.

Sequence in context: A174715 A069817 A071439 * A082119 A129708 A071518

Adjacent sequences: A100938 A100939 A100940 * A100942 A100943 A100944

KEYWORD

cons,nonn

AUTHOR

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 23 2004

STATUS

approved