A090142 -id:A090142 - cp's OEIS frontend

A116938 Expansion of e^2 in base 2.

1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0

Offset: 3

Jonathan Vos Post, Mar 21 2006

			111.010001000000 (base 2) ~ 7.389056098930650... (base 10) ~ e^2. 100 decimal places precision here.

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3.
Eli Maor, e: The Story of a Number, Princeton Univ. Press, 1994.

John Cosgrave, links to "New Proofs of the Irrationality of e^2 and e^4."

Cf. A001113 (e), A072334 (e^2), A090142 (e^2-e).
Cf. A090143 (e^3-2e^2+e/2), A089139 (e^4-3e^3+2e^2-e/6), A090143 (e^3-2e^2+e/2).
Cf. A001671 (powers of e rounded up), A107586 (powers of e^(1/e) rounded up).

RealDigits[E^2, 2, 100] (* Stefan Steinerberger, Mar 30 2006 *)

A370563 Decimal expansion of expected number of trials needed for the sum of uniform random variables from the interval [0,1] to exceed e.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, May 01 2024

			6.104002341363754151667232902275147659559194262...

J. Uspensky, Introduction to Mathematical Probability (1937), 277-278.

Cf. A089087, A090142.

u=N[E^(E - 2)*(4 + (E - 2)*E)/2, 100]; First[RealDigits[u]]
N[Mean[Table[Length[NestWhileList[# + RandomReal[1] &, 0, #1 < E &]] - 1, 10^5]]] (* sample mean *)  (* Peter J. C. Moses, Apr 30 2024 *)

Equals e*(e-2)*(4 +(e-2)*e)/2.

cp's OEIS Frontend

A116938 Expansion of e^2 in base 2.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica