A074948 -id:A074948 - cp's OEIS frontend

A074952 Continued fraction for sqrt((Pi^2 + e^2)/2).

2, 1, 15, 54, 15, 1, 2, 2, 1, 2, 19, 3, 2, 1, 1, 19, 1, 3, 2, 4, 1, 5, 1, 1, 1, 1, 5, 8, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 9, 2, 3, 18, 5, 63, 2, 1, 1, 4, 13, 3, 10, 1, 5, 1, 20, 1, 6, 1, 38, 2, 1, 4, 57, 1, 8, 12, 9, 2, 1, 2, 1, 1, 4, 10, 1, 1, 1, 15, 2, 4, 1, 1, 1, 1, 9, 2, 2, 3, 54, 1, 39, 1, 1, 5

Offset: 0

Zak Seidov, Oct 05 2002

Curiously enough sqrt((Pi^2 + e^2)/2) = 2.937572169 is roughly the distance (in AU) from the Sun of the asteroid 407 Arachne. - Zak Seidov, Oct 03 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..999

Cf. A074948 (decimal expansion).

ContinuedFraction[Sqrt[(E^2 + Pi^2)/2], 70] (* Zak Seidov, Oct 03 2013 *)

contfrac(sqrt((Pi^2+exp(1)^2)/2)) \\ Michel Marcus, Oct 03 2013

Corrected and edited by Zak Seidov, Oct 03 2013

Offset changed by Andrew Howroyd, Aug 07 2024

A342209 Decimal expansion of logarithmic mean of Pi and e.

Original entry on oeis.org

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

Offset: 1

Gleb Koloskov, Mar 05 2021

The logarithmic mean of Pi and e lies between the arithmetic and geometric means of Pi and e.

			2.9248335452376948992733592...

B. C. Carlson, The logarithmic mean, The American Mathematical Monthly, 79(6) 1972, pp. 615-618.
Wikipedia, Logarithmic mean.

Cf. A000796 (Pi), A001113 (e), A019645, A074916, A074948, A074950, A074957.

RealDigits[(Pi - E)/(Log[Pi] - 1), 10, 100][[1]] (* Amiram Eldar, Mar 06 2021 *)

PARI
```
(Pi-exp(1))/(log(Pi)-1)
```

Equals (Pi-e)/(log(Pi)-1).

cp's OEIS Frontend

A074952 Continued fraction for sqrt((Pi^2 + e^2)/2).

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