Definition:Stern Number
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Definition
A Stern number is an odd number which can not be represented in the form:
- $2 a^2 + p$
where:
- $a \in \Z_{>0}$ is a (strictly) positive integer
- $p$ is a prime number.
Sequence
The sequence of Stern numbers begins:
- $1, 3, 17, 137, 227, 977, 1187, 1493, 5777, 5993$
It is not known whether there are any more.
Also see
- Results about Stern numbers can be found here.
Source of Name
This entry was named for Moritz Abraham Stern.
Historical Note
On reading about Goldbach's Lesser Conjecture in $1856$, Moritz Abraham Stern and his students tested all the primes to $9000$, and found the counterexamples $5777$ and $5993$.
He then went on to investigate odd integers that cannot be represented in the form $2 a^2 + p$ where $a > 0$.
The odd integers that he and his students found were named Stern numbers by Laurent Hodges in his $1993$ paper which summarised the findings on this topic.
Sources
- 1993: Laurent Hodges: A Lesser-Known Goldbach Conjecture (Math. Mag. Vol. 66: pp. 45 – 47) www.jstor.org/stable/2690477