Joshua Taylor - cp's OEIS frontend

User: Joshua Taylor

Joshua Taylor has authored 2 sequences.

A191220 Decimal expansion of x, where Arithmetic-Geometric Mean of 1 and x = Pi.

6, 5, 6, 1, 7, 6, 3, 4, 3, 5, 5, 8, 6, 8, 3, 5, 3, 5, 9, 9, 1, 7, 8, 0, 0, 1, 5, 7, 8, 1, 5, 2, 3, 0, 3, 9, 0, 8, 9, 0, 4, 7, 9, 0, 4, 2, 8, 0, 0, 6, 8, 6, 5, 5, 1, 3, 1, 9, 2, 4, 4, 8, 6, 0, 3, 0, 5, 5, 2, 9, 1, 4, 0, 1, 5, 3, 7, 5, 7, 7, 9, 4, 3, 5, 3, 3, 0, 0, 6, 9, 0, 8, 9, 9, 6, 9, 7, 1, 5, 6, 4, 8, 3, 3, 9, 5, 9, 8, 4, 7

Offset: 1

Joshua Taylor, May 26 2011

SetPrecision[
Nest[((x - (ArithmeticGeometricMean[1, x] - Pi)/
        D[ArithmeticGeometricMean[1, x] - Pi, x]) /. x -> #1) &, 6,
  5], 50]

PARI
```
\p 120
solve(x=5,10,agm(x,1)-Pi)
```

A140663 Decimal expansion of the number x defined by x^(x^x) = 27.

Original entry on oeis.org

2, 0, 7, 1, 9, 6, 9, 2, 2, 9, 0, 8, 2, 3, 1, 2, 9, 1, 5, 2, 3, 4, 1, 9, 0, 5, 5, 6, 3, 6, 3, 2, 9, 5, 7, 7, 7, 8, 5, 3, 5, 3, 3, 8, 0, 7, 5, 9, 5, 4, 1, 1, 6, 2, 2, 7, 1, 7, 4, 9, 0, 8, 1, 8, 3, 9, 4, 6, 6, 6, 1, 0, 9, 8, 5, 2, 7, 7, 3, 4, 0, 0, 6, 9, 0, 0, 6, 6, 5, 7, 7, 5, 4, 6, 3, 0, 9, 8, 5, 3, 8, 5, 4, 6, 2

Offset: 1

Joshua Taylor, Jul 11 2008

			2.07196922908231...

Cf. A093590.

Digits := 120: x := 2.071 : for i from 1 to 30 do xxx := x^(x^x) : n := xxx-27 : d := xxx*(x^x*log(x)*(1+log(x))+x^(x-1)) ; x := evalf(x-n/d) ; print(x) ; od: # R. J. Mathar, Aug 08 2008

digits = 105; x0 = x /. FindRoot[x^(x^x) == 27, {x, 2}, WorkingPrecision -> digits+1]; RealDigits[x0, 10, digits][[1]] (* Jean-François Alcover, Jan 28 2014 *)

Extended beyond 15 digits by R. J. Mathar, Aug 08 2008

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User: Joshua Taylor

A191220 Decimal expansion of x, where Arithmetic-Geometric Mean of 1 and x = Pi.

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A140663 Decimal expansion of the number x defined by x^(x^x) = 27.

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