--- In

primenumbers@yahoogroups.com, "Maximilian Hasler" <maximilian.hasler@...> wrote:

>

> > Format: (n, number of m less than n such that 2^m+3^n or 2^n+3^m is prime)

> >

> > (1,1) (2,2) (3,2) (4,3) (5,3) (6,3) (9,3) (11,3) (25,2)

> > (33,3) (34,3) (54,1) (69,2) (70,3) (97,3) (103,3) (115,3)

> > (...)

> > (951,3) (958,3) (966,1) (970,3)

>

> Very cool. To notch it up on the coolness factor one could submit this sequence to OEIS.

>

> Modulo correcting "less than" to "not exceeding" (or specifying that m may be zero, or correcting a(1)=0 and others in the above).

>

> Actually there are at least 6 sequences:

> MU = { n | MU1(n)<=3 } (or why not <= 2 or even <= 1 ?)

> MU1(n) = # { m <= n | 2^n+3^m or 2^m+3^n is prime } (or "<" ?)

> MU2(n) = min { m | 2^n+3^m or 2^m+3^n is prime }

> MU3(n) = max { m <= n | 2^n+3^m or 2^m+3^n is prime } (or "<" ?)

> MU4(n) = min { m | 2^n+3^m is prime }

> MU5(n) = min { m | 2^m+3^n is prime }

>

>

> I checked that they are not in OEIS except for MU5 :

>

> A123359 Least m such that 3^n+2^m is prime.

>

> But maybe better double-check...

>

> Maximilian

>

Thank you Maximilian,

The OESIS thing would only be appealing to me if the minimum m that caused

2^n+3^m or 2^m+3^n to be prime was always found to be less than n for all n.

Then I might consider adding the sequence

1,54,129,135,170,175,185,274,280,335,460,489,547,611, 614,...

These are the n such that only one m less than n makes 2^n+3^m or 2^m+3^n prime.

So far, so good. Up to n=1420 there is at least one m < n that that makes a prime.

Mark