A073226 -id:A073226 - cp's OEIS frontend

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

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

A093592 Decimal expansion of e^(3*e).

Original entry on oeis.org

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

Offset: 4

Mohammad K. Azarian, May 14 2004

			3480.20154171382945022163122422

Harry J. Smith, Table of n, a(n) for n = 4..20000

Cf. A001113, A073226, A073230.

{ default(realprecision, 20080); x=exp(1)^(3*exp(1))/1000; for (n=4, 20000, d=floor(x); x=(x-d)*10; write("b093592.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

A093606 Decimal expansion of e^(4*e).

Original entry on oeis.org

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

Offset: 5

Mohammad K. Azarian, May 14 2004

			52739.88681633180803709993389141467732514937068739418340790649588568704...

Harry J. Smith, Table of n, a(n) for n = 5..20000

Cf. A001113, A073226, A073230.

RealDigits[E^(4E),10,120][[1]]  (* Harvey P. Dale, Apr 29 2011 *)

{ default(realprecision, 20080); x=exp(1)^(4*exp(1))/10000; for (n=5, 20000, d=floor(x); x=(x-d)*10; write("b093606.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

Offset corrected from 1 to 5 and example updated by Harry J. Smith, Jun 19 2009

A093619 Decimal expansion of e^(-2*e).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, May 14 2004

			0.004354420874722252279677

Harry J. Smith, Table of n, a(n) for n = 0..20000

Cf. A001113, A073226, A073230.

Join[{0,0},RealDigits[E^(-2E),10,120][[1]]] (* Harvey P. Dale, Jan 22 2016 *)

{ default(realprecision, 20080); x=10*exp(1)^(-2*exp(1)); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b093619.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

A093624 Decimal expansion of e^(-3*e).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, May 14 2004

			0.000287339680766749155

Harry J. Smith, Table of n, a(n) for n = 0..20000

Cf. A001113, A073226, A073230.

Join[{0,0,0},RealDigits[E^(-3E),10,120][[1]]] (* Harvey P. Dale, Aug 02 2017 *)

{ default(realprecision, 20080); x=10*exp(1)^(-3*exp(1)); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b093624.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

A093626 Decimal expansion of e^(-4*e).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, May 14 2004

			0.000018960981154216904682363860800

Harry J. Smith, Table of n, a(n) for n = 0..20000

Cf. A001113, A073226, A073230.

Join[{0,0,0,0},RealDigits[1/(E^(4E)) ,10,120][[1]]] (* Harvey P. Dale, Jan 17 2023 *)

{ default(realprecision, 20080); x=10*exp(1)^(-4*exp(1)); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b093626.txt", n, " ", d)); } \\ Harry J. Smith, Jun 19 2009

A187079 Decimal expansion of (sqrt(2 + e^e)/e)^e.

Original entry on oeis.org

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

Offset: 1

Arkadiusz Wesolowski, Mar 08 2011

(sqrt(2 + e^e)/e)^e is an approximation to Pi that's correct to five decimal digits.

			(sqrt(2+e^e)/e)^e = 3.141599009451764738125397155...

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
Carlos Rivera, Puzzle 50

Cf. A000796, A073227, A073226.

SetDefaultRealField(RealField(100)); (Sqrt(2+Exp(Exp(1)))/Exp(1))^Exp(1); // G. C. Greubel, Sep 29 2018

evalf((sqrt(2+exp(1)^exp(1))/exp(1))^exp(1),120); # Muniru A Asiru, Sep 29 2018

RealDigits[N[(Sqrt[2 + E^E]/E)^E, 200]][[1]] (* Arkadiusz Wesolowski, Mar 08 2011 *)

default(realprecision, 200); e=exp(1); x=(sqrt(2+e^e)/e)^e; for(n=1, 200, d=floor(x); x=(x-d)*10; print1(d, ", ")); \\ Arkadiusz Wesolowski, Mar 08 2011

A202949 Decimal expansion of (e^e)^(e^e), where e=exp(1).

Original entry on oeis.org

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

Offset: 18

M. F. Hasler, Dec 26 2011

			776486517915808457.38262707214480111269813738740893733361098023776562998338874696481792585472289...

Cf. A073226, A073227, A073228, A085667, A181180, A073232. - M. F. Hasler, Dec 26 2011

RealDigits[#^#&/@(E^E),10,120][[1]] (* Harvey P. Dale, Aug 31 2023 *)

default(realprecision,99); t=exp(1); t=t^t; t=t^t

A073226^A073226.

A226776 Decimal expansion of the maximum value of f(x) = x - log(x)^log(x).

Original entry on oeis.org

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

Offset: 1

Richard R. Forberg, Jun 17 2013

The value of x where f(x) is maximum is 8.06157... Note that greater precision in this value is made difficult due to a broad "flat" maximum.
In the recursive formula:  b(n+1) = log(b(n))^log(b(n)) + c, where c is a constant, the maximum value of c, without the recursion diverging to infinity, is maximum value of the function above (3.4172192....), with b(1) set anywhere in the range 1 < b(1) <= 8.06157.
At values of c between 3.4172192 +/- 0.0000005 demonstrable convergence or divergence of the recursion above takes tens of thousands of iterations, increasing with further closeness to 3.4172192517331..., if b(1) is within the range above.
At x = e^e = 15.1542... (see A073226), the function f(x) = 0. This is the only value for b(1) where the recursion above is stable when c = 0.

			3.4172192517331903782941430626511991141665169728869621034583784206062...

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

digits = 92; FindMaximum[x-Log[x]^Log[x], {x, 3}, WorkingPrecision -> digits] // First // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 20 2014 *)

(x->x-log(x)^log(x))(solve(x=8,9,my(L=log(x));1-L^L*(1+log(L))/x)) \\ Charles R Greathouse IV, Jun 18 2013

A235214 Decimal expansion of exp(exp(1) + 1).

Original entry on oeis.org

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

Offset: 2

Richard R. Forberg, Jan 04 2014

May also be written as e*(e^e).

			41.19355567471612356318828...

Ovidiu Furdui, Solution to problem 91.H, Mathematical Gazette 92(523), 2008, pp. 174-175.

Cf. A005493, A234473 (e^e/e), A073226 (e^e), A001113 (e).

Cf. A061354, A061355.

RealDigits[E^(E + 1), 10, 100][[1]] (* Alonso del Arte, Jan 05 2014 *)

exp(exp(1)+1) \\ Charles R Greathouse IV, Jan 14 2014

Equals Sum_{n>=0} A005493(n)/n!.
Equals 2*lim_{n->oo} n*(exp(Sum_{k=0..n} 1/k!) - ((1+1/n)^n)^e). See the Mathematical Gazette link. - Michel Marcus, Oct 24 2017
Equals Sum_{k>=1} e^k/(k-1)!. - Amiram Eldar, Jul 28 2020

More terms from Rick L. Shepherd, Jan 25 2014

cp's OEIS Frontend

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

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A093592 Decimal expansion of e^(3*e).

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A093606 Decimal expansion of e^(4*e).

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Extensions

A093619 Decimal expansion of e^(-2*e).

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A093624 Decimal expansion of e^(-3*e).

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A093626 Decimal expansion of e^(-4*e).

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A187079 Decimal expansion of (sqrt(2 + e^e)/e)^e.

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A202949 Decimal expansion of (e^e)^(e^e), where e=exp(1).

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