A073239 -id:A073239 - cp's OEIS frontend

A073233 Decimal expansion of Pi^Pi.

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

Offset: 2

Rick L. Shepherd, Jul 21 2002

A weak form of Schanuel's Conjecture implies that Pi^Pi is transcendental--see Marques and Sondow (2012).

			36.4621596072079117709908260226...

Harry J. Smith, Table of n, a(n) for n = 2..20000
D. Marques and J. Sondow, The Schanuel Subset Conjecture implies Gelfond's Power Tower Conjecture, arXiv:1212.6931 [math.NT], 2012-2013.

Cf. A000796 (Pi), A073234 (Pi^Pi^Pi), A073237 (ceil(Pi^Pi^...^Pi), n Pi's), A073238 (Pi^(1/Pi)), A073239 ((1/Pi)^Pi), A073240 ((1/Pi)^(1/Pi)), A073243 (limit of (1/Pi)^(1/Pi)^...^(1/Pi)), A073236 (Pi analog of A004002).
Cf. A073226 (e^e).
Cf. A049006 (i^i), A116186 (real part of i^i^i).
Cf. A194555 (real part of i^e^Pi).

RealDigits[N[Pi^Pi,200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

PARI
```
Pi^Pi
```

{ default(realprecision, 20080); x=Pi^Pi/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b073233.txt", n, " ", d)); } \\ Harry J. Smith, Apr 30 2009

A073238 Decimal expansion of Pi^(1/Pi).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jul 25 2002

Pi^(1/Pi) = 1/((1/Pi)^(1/Pi)) (reciprocal of A073240).

			1.43961949584759068833649080497...

Cf. A000796 (Pi), A049541 (1/Pi), A073239 ((1/Pi)^Pi), A073240 ((1/Pi)^(1/Pi)), A073233 (Pi^Pi).

RealDigits[N[Pi^(1/Pi),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

PARI
```
Pi^(1/Pi)
```

A073240 Decimal expansion of (1/Pi)^(1/Pi).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jul 27 2002

(1/Pi)^(1/Pi) = Pi^(-1/Pi) = 1/(Pi^(1/Pi)) (reciprocal of A073238).

			0.69462799224682615312438376141...

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000796 (Pi), A049541 (1/Pi), A073241 ((1/Pi)^(1/Pi)^(1/Pi)), A073243 (limit of (1/Pi)^(1/Pi)^...^(1/Pi)), A073238 (Pi^(1/Pi)), A073239 ((1/Pi)^Pi), A073233 (Pi^Pi).

First[RealDigits[(1/Pi)^(1/Pi),10,100]] (* Paolo Xausa, Nov 07 2023 *)

PARI
```
(1/Pi)^(1/Pi)
```

cp's OEIS Frontend

A073233 Decimal expansion of Pi^Pi.

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A073238 Decimal expansion of Pi^(1/Pi).

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A073240 Decimal expansion of (1/Pi)^(1/Pi).

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