A342209 Decimal expansion of logarithmic mean of Pi and e.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..108.

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

Wikipedia, Logarithmic mean.

Formula

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

Example

2.9248335452376948992733592...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A010597 A245253 A153460 * A248695 A221139 A217273

Adjacent sequences: A342206 A342207 A342208 * A342210 A342211 A342212

Keyword

nonn,cons

Author

Gleb Koloskov, Mar 05 2021

Status

approved