a property of multisets: unit fractions with a twist

[hv at crypt.org]

By definition, your answer would seem to be:

A018252  The nonprime numbers (1 together with the composite numbers
of A002808).
	1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27,
28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50,
51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72,
74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88

On 12/11/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> "Compact" here means the smallest difference between terms. One candidate is
> A052548: 3, 4, 6, 10, 18, etc. It is easy to show that there is one prime
> between successive members of this sequence by application of Bertrand's
> Postulate (at least one prime between n and 2n - 2, n >=3):
>
> 3, 3*2 - 2 = 4
> 4, 4*2 - 2 = 6
> 6, 6*2 - 2 = 10
>
> etc.
>
> Are there any sequences more "compact" than this that can be proved to have
> primes between successive members?
>
>
>         -Andrew Plewe-
>
>
>
>



This fails because a.) there isn't at least one prime between 8 and 9, 14
and 15, etc. and b.) there is no way to determine (other than via brute
force) that there will be at least one prime between a(n) and a(n+1) in
those cases where there is a gap.


-----Original Message-----
between a(n) and a(n+1)

By definition, your answer would seem to be:

A018252  The nonprime numbers (1 together with the composite numbers
of A002808).
28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50,
51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72,
74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88

On 12/11/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> "Compact" here means the smallest difference between terms. One candidate
is
> A052548: 3, 4, 6, 10, 18, etc. It is easy to show that there is one prime
> between successive members of this sequence by application of Bertrand's
> Postulate (at least one prime between n and 2n - 2, n >=3):
>
> 3, 3*2 - 2 = 4
> 4, 4*2 - 2 = 6
> 6, 6*2 - 2 = 10
>
> etc.
>
> Are there any sequences more "compact" than this that can be proved to
have
> primes between successive members?
>
>
>         -Andrew Plewe-
>
>
>
>