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A113554 Decimal expansion of average of e^(1/e) and Pi. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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

(Sage) 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 A021440 A271524

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

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Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)