A071810

[franktaw at netscape.net]

Sorry, I confused myself about 11 - it is the largest number not the 
sum of 2 or more distinct primes, but it is, of course, prime.

So the formula should be: a(n) = PrimePi(N) - isprime(N-1) - 
isprime(N-4) - isprime(N-6), where N = sum_{k=1}^n Prime(k).

Franklin T. Adams-Watters


-----Original Message-----
From: maxale at gmail.com
To: franktaw at netscape.net
Cc: seqfan at ext.jussieu.fr
Sent: Thu, 7 Sep 2006 11:58 PM
Subject: Re: A071810

  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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