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

Author

Gleb Koloskov, Mar 05 2021

Keywords

• nonn
• cons

Comments

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

Examples

			2.9248335452376948992733592...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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