A071810

[Max A.]

Franklin,

Your formula does not match numerical values.
The sequence I suggested is:

1, 3, 4, 5, 9, 12, 16, 19, 25, 31, 37, 43, 51, 59, 66, 75, 84, 95,
103, 115, 127, 137, 150, 162, 177, 191, 205, 218, 233, 250, 267, 282,
299, 319, 338, 359, 376, 399, 421, 440, 461, 481, 508, 531, 556, 578,
602, 629, 653, 683

while your formula gives:

0, 2, 3, 4, 7, 11, 14, 18, 23, 30, 35, 42, 49, 58, 64, 74, 83, 94,
101, 114, 125, 136, 148, 161, 175, 190, 204, 217, 232, 249, 265, 281,
298, 318, 337, 358, 375, 398, 419, 439, 460, 480, 507, 530, 555, 577,
601, 628, 651, 682

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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