A073230 -id:A073230 - cp's OEIS frontend

A073226 Decimal expansion of e^e.

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

Offset: 2

Rick L. Shepherd, Jul 21 2002

Given z > 0, there exist positive real numbers x < y, with x^y = y^x = z, if and only if z > e^e. In that case, 1 < x < e < y and (x, y) = ((1 + 1/t)^t, (1 + 1/t)^(t+1)) for some t > 0. (For example, t = 1 gives 2^4 = 4^2 = 16 > e^e.) Proofs of these classical results and applications of them are in Marques and Sondow (2010).
e^e = lim_{n->infinity} ((n+1)/n)^((n+1)^(n+1)/n^n), n > 0 an integer; cf. [Vernescu] wherein it is also stated that the assertions of the previous comment above were proved by Alexandru Lupas in 2006. - L. Edson Jeffery, Sep 18 2012
A weak form of Schanuel's Conjecture implies that e^e is transcendental--see Marques and Sondow (2012).

			15.15426224147926418976043027262991190552854853685613976914...

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.
Simon Plouffe, exp(E) to 2000 places
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164.
A. Vernescu, About the use of a result of Professor Alexandru Lupas to obtain some properties in the theory of the number e, Gen. Math., Vol. 15, No. 1 (2007), 75-80.

Cf. A073233 (Pi^Pi), A049006 (i^i), A001113 (e), A073227 (e^e^e), A004002 (Benford numbers), A056072 (floor(e^e^...^e), n e's), A072364 ((1/e)^(1/e)), A030178 (limit of (1/e)^(1/e)^...^(1/e)), A073229 (e^(1/e)), A073230 ((1/e)^e).

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

Mathematica
```
RealDigits[ E^E, 10, 110] [[1]]
```
PARI
```
exp(exp(1))
```

{ default(realprecision, 20080); x=exp(1)^exp(1)/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b073226.txt", n, " ", d)); } \\ Harry J. Smith, Apr 30 2009

Equals Sum_{n>=0} e^n/n!. - Richard R. Forberg, Dec 29 2013

Equals Product_{n>=0} e^(1/n!). - Amiram Eldar, Jun 29 2020

A073229 Decimal expansion of e^(1/e).

Original entry on oeis.org

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

Offset: 1

Rick L. Shepherd, Jul 22 2002

e^(1/e) = 1/((1/e)^(1/e)) (reciprocal of A072364).
Let w(n+1)=A^w(n); then w(n) converges if and only if (1/e)^e <= A <= e^(1/e) (see the comments in A073230) for initial value w(1)=A. If A=e^(1/e) then lim_{n->infinity} w(n) = e. - Benoit Cloitre, Aug 06 2002; corrected by Robert FERREOL, Jun 12 2015
x^(1/x) is maximum for x = e and the maximum value is e^(1/e). This gives an interesting and direct proof that 2 < e < 4 as 2^(1/2) < e^(1/e) > 4^(1/4) while 2^(1/2) = 4^(1/4). - Amarnath Murthy, Nov 26 2002
For large n, A234604(n)/A234604(n-1) converges to e^(1/e). - Richard R. Forberg, Dec 28 2013
Value of the unique base b > 0 for which the exponential curve y=b^x and its inverse y=log_b(x) kiss each other; the kissing point is (e,e). - Stanislav Sykora, May 25 2015
Actually, there is another base with such property, b=(1/e)^e with kiss point (1/e,1/e). - Yuval Paz, Dec 29 2018
The problem of finding the maximum of f(x) = x^(1/x) was posed and solved by the Swiss mathematician Jakob Steiner (1796-1863) in 1850. - Amiram Eldar, Jun 17 2021

			1.44466786100976613365833910859...

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 35.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Ovidiu Furdui, Problem 11982, The American Mathematical Monthly, Vol. 124, No. 5 (2017), p. 465; A Limit of a Power of a Sum, Solution to Problem 11982 by Roberto Tauraso, ibid., Vol. 126, No. 2 (2019), p. 187.
Simon Plouffe, exp(1/e).
Jonathan Sondow and Diego Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae, Vol. 37 (2010), pp. 151-164; see Definition 4.1 on p. 158.
Jacob Steiner, Über das größte Product der Theile oder Summanden jeder Zahl, Crelle, Vol. 40 (1850), pp. 208; alternative link.
Eric Weisstein's World of Mathematics, Steiner's Problem.

Cf. A001113 (e), A068985 (1/e), A073230 ((1/e)^e), A072364 ((1/e)^(1/e)), A073226 (e^e).
Cf. A093157, A103476.
Cf. A038051, A086331, A252782, A270593, A270917, A270923, A277473, A309652, A332408.

evalf[110](exp(exp(-1))); # Muniru A Asiru, Dec 29 2018

Mathematica
```
RealDigits[ E^(1/E), 10, 110] [[1]]
```
PARI
```
exp(1)^exp(-1)
```

Equals 1 + Integral_{x = 1/e..1} (1 + log(x))/x^x dx = 1 - Integral_{x = 0..1/e} (1 + log(x))/x^x dx. - Peter Bala, Oct 30 2019
Equals Sum_{k>=0} exp(-k)/k!. - Amiram Eldar, Aug 13 2020
Equals lim_{x->oo} (Sum_{n>=1} (x/n)^n)^(1/x) (Furdui, 2017). - Amiram Eldar, Mar 26 2022

A072364 Decimal expansion of (1/e)^(1/e).

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jul 18 2002

Minimum value of x^x for real x>0.
Also minimum value of 1/x^(1/x) for real x>0 (occurs at e). Equals exp(Pi)/exp(1/exp(1)) * exp(-Pi). - Gerald McGarvey, Sep 21 2004
If (1/e)^(1/e) < y < 1, then x^x = y has two solutions x = a and x = b with 0 < a < 1/e < b < 1. For example, (1/e)^(1/e) < 1/sqrt(2) < 1 and (1/4)^(1/4) = (1/2)^(1/2) = 1/sqrt(2) with 1/4 < 1/e < 1/2. - Jonathan Sondow, Sep 02 2011

			0.69220062755534635386...

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 26, page 233.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Alex Chin et al., Pick a Tree-Any Tree, The American Mathematical Monthly, 122.5 (2015): 424-432.
Plouffe's Inverter entry for .69220062755.
Jonathan Sondow and Diego Marques, Algebraic and transcendental solutions of some exponential equations, arXiv:1108.6096 [math.NT], 2011; Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 3 in the link.

Cf. A068985 (1/e), A001113 (e), A072365 ((1/3)^(1/3)), A073229 (e^(1/e)), A073230 ((1/e)^e).

Cf. also A258707.

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

evalf(exp(-1/exp(1)), 120);  # Alois P. Heinz, Oct 26 2021

Mathematica
```
RealDigits[E^(-1/E), 10, 111][[1]]
```
PARI
```
(1/exp(1))^(1/exp(1))
```

exp(-1/exp(1)) \\ Charles R Greathouse IV, Sep 01 2011

From Amiram Eldar, Aug 19 2020: (Start)
Equals Sum_{k>=0} (-1)^k/(exp(k)*k!).
Equals Product_{k>=0} exp((-1)^(k+1)/k!). (End)

A073243 Decimal expansion of exp(-LambertW(log(Pi))), solution to x = 1/Pi^x.

Original entry on oeis.org

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

Offset: 0

Rick L. Shepherd, Jul 28 2002

Original definition: Limit of (1/Pi)^...^(1/Pi), n times, as n approaches infinity. Equals exp(-LambertW(log(Pi))).
The value can be obtained by iterating x -> 1/Pi^x with any real starting value, but convergence is linear and slow: about 5 iterations are needed for each additional decimal digit. - M. F. Hasler, Nov 01 2011
According to the Weisstein link, infinite iterated exponentiation such as used here, which is referred to both as an "infinite power tower" and "h(x)" -- with graph and other notations -- "converges iff e^(-e) <= x <= e^(1/e) as shown by Euler (1783) and Eisenstein (1844)" (citing Le Lionnais and Wells references). e^(-e) = A073230. e^(1/e) = A073229. x of interest here = 1/Pi = A049541. (1/A073243)^(1/A073243) = A030437^A030437 = Pi.
If y = h(x) = x^x^x^... converges, then by substitution y = x^y. So x^x^x^... is a solution y to the equation y^(1/y) = x. - Jonathan Sondow, Aug 27 2011
The expressions involving "..." in the above comment are misleading, since the limit is not obtained by applying additional "^x" to the previous expression, i.e., iterating "t -> t^x", but corresponds to iterations of "t -> x^t". - M. F. Hasler, Nov 01 2011

			0.53934349886230120806079568445...

Stanislav Sykora, Table of n, a(n) for n = 0..1999
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see the Appendix, arXiv:1108.6096.
Eric Weisstein's World of Mathematics, Power Tower

Cf. A000796 (Pi), A049541 (1/Pi), A073240 ((1/Pi)^(1/Pi)), A073241 ((1/Pi)^(1/Pi)^(1/Pi)), A030437 (reciprocal of A073243), A030178 (corresponding limit for 1/e), A030797 (reciprocal of A030178).

y /. FindRoot[y^(1/y) == 1/Pi, {y, 1}, WorkingPrecision -> 100] (* Jonathan Sondow, Aug 27 2011 *)
First[RealDigits[Exp[-ProductLog[Log[Pi]]], 10, 104]] (* Vladimir Reshetnikov, Nov 01 2011 *)

/* The program below was run with precision set to 1000 digits */ /* n is the number of iterated exponentiations performed. */ /* (n turns out to be 954 with 1E-200 specified here) */ n=0; s=1/Pi; t=1; while(abs(t-s)>1E-200, t=s; s=(1/Pi)^s; n++); print(n,",",s)

solve(x=0,1,x-1/Pi^x)  \\ M. F. Hasler, Nov 01 2011

x = LambertW(log(Pi))/log(Pi), solution to Pi^x=1/x. - M. F. Hasler, Nov 01 2011

A061481 a(n) = floor(e^(n/e)).

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 9, 13, 18, 27, 39, 57, 82, 119, 172, 249, 359, 520, 751, 1085, 1568, 2265, 3272, 4727, 6830, 9867, 14255, 20593, 29751, 42980, 62092, 89703, 129591, 187216, 270465, 390733, 564479, 815485, 1178106, 1701972, 2458784, 3552126, 5131643

Offset: 0

Amarnath Murthy, May 05 2001

nonn

Integer part of the maximal product possible among numbers (not restricted to integers) that sum to n. Note that a(n) >= A000792(n).

Ignoring the first term, for n >= 1, 1,2,3,4,6,9,... is the maximal integer such that its positive real n-th root in an infinite power tower converges to a limit; e.g., for n=5, 6 is the maximal such integer and (6^(1/5))^((6^(1/5))^((6^(1/5))^(...))) converges (to 2.1991359...). Similar infinite power towers with the 5th roots of 1,2,3,4,5, respectively also converge. See comments and links associated with A073229 and A073230. These terms are also the numbers of such converging infinite power towers composed of n-th roots of positive integers. Disregarding the trivial power tower of 1s, 2 is the unique positive integer whose infinite power tower of its square root converges; the limit is 2 itself. - Rick L. Shepherd, Sep 30 2007

Harry J. Smith, Table of n, a(n) for n = 0..500
E. F. Krause, Maximizing The Product of Summands, Mathematics Magazine, MAA Oct 1996, Vol. 69, no. 5 pp. 270-271.
D. J. Newman, A Problem Seminar, Problem 15 pp. 5; 15 Springer-Verlag NY 1982.

Cf. A107586.

Cf. A073229, A073230.

Table[ Floor[E^(n/E)], {n, 0, 35}] (* Robert G. Wilson v, Oct 23 2004 *)

{ default(realprecision, 100); e=exp(1); for (n=0, 500, write("b061481.txt", n, " ", floor(e^(n/e))) ) } \\ Harry J. Smith, Jul 23 2009

A194346 Decimal expansion of h_o(1/17), where h_o(x) is the odd infinite power tower function.

Original entry on oeis.org

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

Offset: 0

Jonathan Sondow, Aug 27 2011

The odd infinite power tower function is h_o(x) = lim f(n,x) as n --> infinity, where f(n+1,x) = x^x^(f(n,x)) and f(1,x) = x. The even infinite power tower function h_e(x) is the same limit except with f(1,x) = x^x (see A194347). The limits exist if and only if 0 < x <= e^(1/e). If (1/e)^e <= x <= e^(1/e), then h_o(x) = h_e(x) = h(x) (the infinite power tower function-see the comments in A073230) and y = h(x) is a solution of x^y = y. If 0 < x < (1/e)^e, then h_o(x) < h_e(x), and two solutions of x^x^y = y are y = h_o(x) and y = h_e(x). For example, y = h_o(1/16) = 1/4 and y = h_e(1/16) = 1/2 are solutions of (1/16)^(1/16)^y = y.

h_o(1/17) and h_e(1/17) are irrational, and at least one of them is transcendental (see Sondow and Marques 2010).

			0.204274736665518499175698745186446957991668690348422572736592466759324966133336...

See the References in Sondow and Marques 2010.

G. C. Greubel, Table of n, a(n) for n = 0..10000
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see Definition 4.3, Figure 7, and top of p. 163.

Cf. A073229, A073230, A073243, A194347.

a = N[1/17, 100]; Do[a = (1/17)^(1/17)^a, {3000}]; RealDigits[a, 10, 100] // First
RealDigits[ Fold[ N[#2^#1, 128] &, 1/17, Table[1/17, {5710}]], 10, 105][[1]] (* Robert G. Wilson v, Mar 20 2012 *)

solve(x=0,1,17^(-17^-x)-x) \\ Charles R Greathouse IV, Mar 20 2012

A334399 Decimal expansion of sinh(e).

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Apr 26 2020

			(e^e - e^(-e))/2 = 7.54413710281697582634182004251653274...

Cf. A001113, A073226, A073230, A073742, A085659, A334400.

Mathematica
```
RealDigits[Sinh[E], 10, 110] [[1]]
```

Equals Sum_{k>=0} e^(2*k+1)/(2*k+1)!.

A334400 Decimal expansion of cosh(e).

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Apr 26 2020

			(e^e + e^(-e))/2 = 7.6101251386622883634186102301133791...

Cf. A001113, A073226, A073230, A073743, A085660, A334399.

Mathematica
```
RealDigits[Cosh[E], 10, 110] [[1]]
```

Equals Sum_{k>=0} e^(2*k)/(2*k)!.

A052110 Decimal expansion of c^c^c^... where c is the constant defined in A037077.

Original entry on oeis.org

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

Offset: 0

Marvin Ray Burns Jan 20 2000, Mar 28 2008, Nov 08 2009, Mar 24 2010, Jun 27 2011

See (Weisstein) link on Power Tower.

			0.4619214401644114454085886426141945786350282801364882284434162927358917250...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.

Eric Weisstein's World of Mathematics, Power Tower.
Gus Wiseman, Tetration.
OEIS Wiki, Tetration.
OEIS Wiki, MRB constant.
Wikipedia, Tetration.

Cf. A037077, A000027, A000312, A002488, A073230.

n = 105; M = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity}, WorkingPrecision -> n + 10, Method -> "AlternatingSigns"]; L = Log[M]; N[-ProductLog[-L]/L, n] (* Marvin Ray Burns, Mar 08 2013 *)

default(realprecision,66);
M=sumalt(x=1,(-1)^x*((x^(1/x))-1));
solve(x=.46,.462,x^(1/x)-M)

Simplified definition by Marvin Ray Burns, Mar 08 2013

A093589 Decimal expansion of e^(2*e).

Original entry on oeis.org

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

Offset: 3

Mohammad K. Azarian, May 14 2004

			229.651664083524132509929588

Harry J. Smith, Table of n, a(n) for n = 3..20000

Cf. A001113, A073226, A073230.

RealDigits[E^(2E),10,120][[1]] (* Harvey P. Dale, Sep 28 2011 *)

{ default(realprecision, 20080); x=exp(1)^(2*exp(1))/100; for (n=3, 20000, d=floor(x); x=(x-d)*10; write("b093589.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

cp's OEIS Frontend

A073226 Decimal expansion of e^e.

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A073229 Decimal expansion of e^(1/e).

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A072364 Decimal expansion of (1/e)^(1/e).

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A073243 Decimal expansion of exp(-LambertW(log(Pi))), solution to x = 1/Pi^x.

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A061481 a(n) = floor(e^(n/e)).

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A194346 Decimal expansion of h_o(1/17), where h_o(x) is the odd infinite power tower function.

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