A073231 -id:A073231 - cp's OEIS frontend

A073227 Decimal expansion of e^e^e.

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

Offset: 7

Rick L. Shepherd, Jul 22 2002

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

			3814279.10476022059220921959409...

Harry J. Smith, Table of n, a(n) for n = 7..20000
D. Marques and J. Sondow, The Schanuel Subset Conjecture implies Gelfond's Power Tower Conjecture, arXiv:1212.6931 [math.NT], 2013.

Cf. A001113 (e), A073226 (e^e), A004002 (e^e^...^e, n times, rounded), A073228 ((e^e)^e), A073231 ((1/e)^(1/e)^(1/e)).

Exp(Exp(Exp(1))); // G. C. Greubel, May 29 2018

RealDigits[E^E^E,10,120][[1]] (* Harvey P. Dale, Dec 14 2011 *)

PARI
```
exp(exp(exp(1)))
```

{ default(realprecision, 20080); x=exp(exp(exp(1)))/1000000; for (n=7, 20000, d=floor(x); x=(x-d)*10; write("b073227.txt", n, " ", d)); } \\ Harry J. Smith, Apr 30 2009

A073228 Decimal expansion of (e^e)^e.

Original entry on oeis.org

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

Offset: 4

Rick L. Shepherd, Jul 22 2002

			1618.17799191265350166869122548...

G. C. Greubel, Table of n, a(n) for n = 4..10000

Cf. A001113 (e), A073226 (e^e), A073227 (e^e^e), A073231 ((1/e)^(1/e)^(1/e)), A073232 (((1/e)^(1/e))^(1/e)).

Exp(Exp(1))^Exp(1); // G. C. Greubel, May 29 2018

RealDigits[(E^E)^E, 10, 120][[1]] (* Alonso del Arte, Jul 03 2012 *)

PARI
```
exp(exp(1))^exp(1)
```

(e^e)^e = e^e^2. - Franklin T. Adams-Watters, Jun 20 2014

A073232 Decimal expansion of ((1/e)^(1/e))^(1/e).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jul 22 2002

			0.87342301849311664298903234866...

Cf. A001113 (e), A068985 (1/e), A072364 ((1/e)^(1/e)), A073231 ((1/e)^(1/e)^(1/e)), A073228 ((e^e)^e), A073227 (e^e^e).

RealDigits[((1/E)^(1/E))^(1/E),10,120][[1]]  (* Harvey P. Dale, Apr 21 2011 *)

PARI
```
exp(-exp(-2))
```

Equals e^(-e^(-2)).

cp's OEIS Frontend

A073227 Decimal expansion of e^e^e.

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A073228 Decimal expansion of (e^e)^e.

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A073232 Decimal expansion of ((1/e)^(1/e))^(1/e).

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