Most "compact" sequence such that there is at least one prime between a(n) and a(n+1)

[Andrew Plewe]

what about

t=1;for(i=1,20,print1(t",");t=nextprime(t+1)+1)

1,3,6,8,12,14,18,20,24,30,32,38,42,44,48,54,60,62,68,72,

where the (t+1) ensures that the next prime is strictly in between the terms.

Maximilian
PS: just read the "clarification" - IMHO, minimality cannot be proved
for any nontrivial suggestion.

On Dec 11, 2007 4:07 PM, Robert Israel <israel at math.ubc.ca> wrote:
> What's the prime between 8 and 9 then?
> But how about a(n) = p(n)-1 where p(n) is the n'th odd prime?
>
> Robert Israel                                israel at math.ubc.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel
> University of British Columbia            Vancouver, BC, Canada
>
>
> On Tue, 11 Dec 2007, Jonathan Post wrote:
>
> > 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-
> >>
> >>
> >>
> >>
> >
>