A071810

[Max A.]

Franklin,

It is not clear to me:
1) why each prime <=N is representable as the sum of distinct primes
<= Prime(n).
2) why the primality of N-11 (for example) affects the result.

Thanks,
Max

On 9/7/06, franktaw at netscape.net <franktaw at netscape.net> wrote:
> Every number except 1, 4, 6, and 11 is representable as the sum of
> distinct primes.  So taking N = A007504(n) = sum_{k=1}^n Prime(k), for
> n >= 4 (N >= 28 > 2*11), this is just PrimePi(N) - 1 - isprime(N-1) -
> isprime(N-4) - isprime(N-6) - isprime(N-11).
>
> (Here isprime is A010051, the characteristic function of primes.)
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: maxale at gmail.com
>
> On 9/7/06, Max A. <maxale at gmail.com> wrote:
>
> > The reason why this does not eat a lot of memory is the fact that the
> > set of all numbers representable as the sum of some of the first n
> > primes is rather small.
>
> Suggestion to a new sequence: a(n) = the number of primes
> representable as the sum of some subset of the set of first n primes.
> Is it in OEIS?
> A071810 counts exactly these primes with multiplicities (i.e.,
> counting different representations of the same prime separately).
>
> Max
>
>
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