

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
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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
^
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*++> 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



