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

1,1

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.

Links

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

Formula

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

Example

2.2931302572997796860604912459379665536278824263086794933977336283...

Mathematica

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

Prog

(SageMath) N((pi+exp(exp(-1)))/2, digits=107) # Danny Rorabaugh, Mar 26 2015
(PARI) (exp(exp(-1))+Pi)/2 \\ Charles R Greathouse IV, Mar 10 2016
(Magma) R:= RealField(100); (Pi(R) + Exp(1/Exp(1)))/2; // G. C. Greubel, Aug 31 2018

Crossrefs

Sequence in context: A182106 A308037 A011403 * A085846 A374169 A021440

Adjacent sequences: A113551 A113552 A113553 * A113555 A113556 A113557

Keyword

cons,nonn,easy

Author

Marco Matosic, Jan 13 2006

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

Status

approved