A387697 Decimal expansion of the probability that a Poisson(1) random variable is a power of 2.

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

Offset

0,1

Comments

Real-world example: Monitor background radiation with a Geiger counter. Choose the counting interval t so that the expected number of clicks in an interval of length t is 1 (for example, if the average rate is r clicks per second, take t = 1/r). Then the probability that a random interval of length t contains a power-of-two number of clicks (1, 2, 4, 8, ...) equals this number.

This number is defined as s/e, where s = Sum_{k>=0} 1/(2^k)!, and e is Euler's number.

Links

Table of n, a(n) for n=0..86.

Formula

Equals A387399*A068985.

Example

0.56715659580006783451756065458018335180288...

Mathematica

RealDigits[N[Sum[1/(2^k)!, {k, 0, Infinity}] / E, 120]][[1]] (* Amiram Eldar, Apr 17 2026 *)

Prog

(PARI) suminf(k=0, 1/(2^k)!)/suminf(k=0, 1/k!)

Crossrefs

Cf. A001113, A068985, A387399, A387398.

Sequence in context: A019978 A030178 A038458 * A284361 A267017 A358203

Adjacent sequences: A387694 A387695 A387696 * A387698 A387699 A387700

Keyword

nonn,cons

Author

Daniel Hoyt, Sep 06 2025

Status

approved