A067736 Decimal expansion of exp(3/2).

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

Offset: 1

Author

Alford Arnold, Mar 10 2002

Keywords

• easy
• nonn
• cons

Comments

It is well known that derangements, A000166, are related to exp(1) (cf. A001113). It appears that derangements with minimal cycle size 3 relate to exp(1+1/2). for example, 720/160 = 4.5, 5040/1140 = 4.4210, 40320/8988 = 4.4859, 362880/80864 = 4.4875 the pattern continues - derangements with minimal cycle size 4 appear to relate in the same way to exp(1 + 1/2 +1/3).

Examples

			4.4816890703380648226020554601192758190057498683696...
		

Links

• D. M. Bătinetu-Giurgiu, Problem 4179, Crux Mathematicorum, Vol. 42, No. 8 (2016), p. 357; Solution to Problem 4179 by Kee-Wai Lau, ibid., Vol. 43, No. 8 (2017), p. 369.
• Index entries for transcendental numbers

Crossrefs

Cf. A000142, A000166, A001113, A038205, A047865, A055209.

Programs

Mathematica

RealDigits[Exp[3/2],10,120][[1]] (* Harvey P. Dale, Apr 24 2016 *)

PARI

exp(3/2) \\ Charles R Greathouse IV, Nov 21 2024

Formula

Equals lim_{n->oo} n/A055209(n)^(1/n^2) (Bătinetu-Giurgiu, 2016). - Amiram Eldar, Apr 11 2022

Solution of x = Integral_{t=0..x} log(t^2) dt. - Thomas Scheuerle, Sep 22 2023

Extensions

More terms from Sascha Kurz, Mar 19 2002