[seqfan] Re: Differenes of conscutive primes

[Aai]

Hi Veikko,

may be I miss something, but why is the K-range for a(3) not 9..13 ?

The subsequent primes 23 29 31 37 41 will also produce 1 2 3.

Or even shorter:  K=[10..13] --> primes 29 31 37 41 --> 1 2 3


Thanks



Hallo Veikko Pohjola, je schreef op 13-01-11 20:05:
> Consider the halved differences of consecutive primes (Prime[k+1]-Prime[k])/2, k=2,3,4,.,K. Remove the duplicates and sort to obtain an ordered set {1,2,3,.,a(i)}of all natural numbers from 1 to a(i). The allowed numbers a(i) make up the following sequence: a(i) = 1, 2, 3, 4, 7, 17, 18,.
>
>
>
> Examples:
>
> 2<=K<=3 ->  {1} ->  a(1)=1
>
> 4<=K<=8 ->  {1,2} ->  a(2)=2
>
> 9<=K<=23 ->  {1,2,3} ->  a(3)=3
>
> 24<=K<=29 ->  {1,2,3,4} ->a(4)=4
>
> 46<=K<=98 ->  {1,2,3,4,5,6,7} ->  a(5)=7
>
>
>
> Might there be a continuation for the sequence a(i)?
>
> Veikko
>
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