A071810

[franktaw at netscape.net]

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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