A113554 Decimal expansion of average of e^(1/e) and Pi.

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

Offset: 1

Author

Marco Matosic, Jan 13 2006

Keywords

• cons
• nonn
• easy

Comments

Close to A085846 which is also close to the product Zeta(2...s) and this is itself close to 2e-Pi. The e-th root of e, eRe, is the maximum for any aRa = bRb pair. See A085846. Likewise for a^b = b^a pairs there is a minimum, e^e.

For the Foias constant F satisfying FRF = fRf, F*f is very close to the third zero of the Riemann zeta function.

Examples

			2.2931302572997796860604912459379665536278824263086794933977336283...
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Programs

Magma

R:= RealField(100); (Pi(R) + Exp(1/Exp(1)))/2; // G. C. Greubel, Aug 31 2018

Mathematica

First[RealDigits[N[(E^(1/E) + Pi)/2, 100]]] (* Ryan Propper, Jul 21 2006 *)

PARI

(exp(exp(-1))+Pi)/2 \\ Charles R Greathouse IV, Mar 10 2016

SageMath

N((pi+exp(exp(-1)))/2,digits=107) # Danny Rorabaugh, Mar 26 2015

Formula

Equals (Pi + e^(1/e))/2.

Extensions

a(18)-a(100) from Ryan Propper, Jul 21 2006

a(99)-a(100) corrected and a(101)-a(105) added by Danny Rorabaugh, Mar 26 2015