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A282532 Position where the discrete difference of the Poissonian probability distribution function with mean n takes its lowest value. In case of a tie, pick the smallest value. 0
1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Is this the same as A183299?

Defining the probability for integer value x in a Poisson distribution of integer mean = q>0 as P(q,x) = e^(-q)*(q^x)/x! then P(n, a(n)+1)- P(n, a(n)) <= P(n, k+1)- P(n, k), for every k > 0.

(Very qualitative) Plot of a Poisson Distribution with mean n. The vertical line above a(n) indicates the place where the distribution has its minimum (negative) discrete difference.

P

^

|             *

|           *    *

|         *        *

|        *           *

|       *              *

|      *           |     *

|     *            |        *

|    *             |             *

|  *               |                  *

*-------------+----+----------------------> x

              n   a(n)

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

With the definition of P(q,x) given in Comments, for instance, if n = 8 then

P(8, a(8)+1)-P(8, a(8)) = P(8,11)-P(8,10) = -0.027071

If we now calculate the discrete difference in a(n)+1 we then obtain

P(8,a(8)+2)-P(8,a(8)+1) = P(8,12)-P(8,11) = -0.0240634

and in a(n)-1

P(8,a(8))-P(8,a(8)-1) = P(8,10)-P(8,9) = -0.0248154

Both previous values are larger than the minimum obtained at a(n).

MATHEMATICA

Table[Position[a=Differences@PDF[PoissonDistribution[n], Range[2^10]], Min@a]//Min, {n, 1, 80}]

CROSSREFS

Cf. A183299.

Sequence in context: A139283 A188013 A183299 * A039243 A265187 A039186

Adjacent sequences:  A282529 A282530 A282531 * A282533 A282534 A282535

KEYWORD

nonn

AUTHOR

Andres Cicuttin, Feb 17 2017

STATUS

approved

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Last modified July 28 11:14 EDT 2021. Contains 346326 sequences. (Running on oeis4.)