A073235 -id:A073235 - cp's OEIS frontend

A202955 Decimal expansion of Pi^Pi^Pi^Pi.

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

Offset: 666262452970848504

M. F. Hasler, Dec 26 2011

The offset equals the floor(Pi^Pi^Pi*Log_10(Pi))+1. - Robert G. Wilson v, Mar 13 2014

Whether this number is an integer or not is an open question. It is also an open question whether Pi^Pi^Pi^...^Pi^Pi n times is an integer for any natural n > 4. - Eliora Ben-Gurion, Nov 17 2019

			9.080222455390617769723931713284287746516046358131897359946935926336845199... *10^666262452970848503

Cf. A073236, A085667, A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073235 ((Pi^Pi)^Pi), A202953 ((Pi^Pi)^(Pi^Pi)).

nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[exp*Log10[base], nbrdgt + Floor[Log10[exp]] + 2]], 10, nbrdgt][[1]]; f[Pi, Pi^Pi^Pi] (* Robert G. Wilson v, Mar 13 2014 *)

LP(a,b)=[10^frac(a=log(a)/log(10)*b),a\1] /* returns [m,e] such that a^b = m*10^e */
LP(Pi,Pi^Pi^Pi)

A000796^A073234.

A073234 Decimal expansion of Pi^(Pi^Pi).

Original entry on oeis.org

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

Offset: 19

Rick L. Shepherd, Jul 25 2002

			1340164183006357435.29744912964...

Christopher Creutzig & Walter Oevel, MuPAD Tutorial. Berlin: Springer-Verlag (2004): 339.

Harry J. Smith, Table of n, a(n) for n = 19..20000

Cf. A000796 (Pi), A073233 (Pi^Pi), A202955 (Pi^Pi^Pi^Pi), A073236 (Pi^Pi^...^Pi, n times, rounded), A073235 ((Pi^Pi)^Pi), A073241 ((1/Pi)^(1/Pi)^(1/Pi)).

RealDigits[Pi^Pi^Pi, 10, 100][[1]] (* Alonso del Arte, Jul 03 2012 *)

DIGITS := 100:
float(PI^(PI^PI)) // from Creutzig & Oevel (2004)

PARI
```
Pi^Pi^Pi
```

{ default(realprecision, 20100); x=Pi^Pi^Pi/10^18; for (n=19, 20000, d=floor(x); x=(x-d)*10; write("b073234.txt", n, " ", d)); } \\ Harry J. Smith, May 01 2009, corrected May 19 2009, had -n

A073242 Decimal expansion of ((1/Pi)^(1/Pi))^(1/Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jul 28 2002

			0.89048823592032706709152866456...

Cf. A000796 (Pi), A049541 (1/Pi), A073240 ((1/Pi)^(1/Pi)), A073241 ((1/Pi)^(1/Pi)^(1/Pi)), A073235 ((Pi^Pi)^Pi), A073234 (Pi^Pi^Pi).

RealDigits[ N[(1/Pi^(1/Pi))^(1/Pi), 110]][[1]]

\\ This shorter statement is equivalent to ((1/Pi)^(1/Pi))^(1/Pi): Pi^(-Pi^-2)

A202953 Decimal expansion of x^x with x=Pi^Pi.

Original entry on oeis.org

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

Offset: 57

M. F. Hasler, Dec 26 2011

			887455172183124295874631455225434602688412866765466125005.158854842801290205563781894793427...

Cf. A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073235 ((Pi^Pi)^Pi), A202949 ((e^e)^(e^e)).

With[{x=Pi^Pi},RealDigits[x^x,10,120][[1]]] (* Harvey P. Dale, Dec 31 2011 *)

PARI
```
p(x)=x^x /* then type p(p(Pi)) */
```

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A202955 Decimal expansion of Pi^Pi^Pi^Pi.

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A073234 Decimal expansion of Pi^(Pi^Pi).

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A073242 Decimal expansion of ((1/Pi)^(1/Pi))^(1/Pi).

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A202953 Decimal expansion of x^x with x=Pi^Pi.

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