A247657 Partial sums of primes, but with a twist.

5, 23, 53, 101, 359, 487, 631, 1669, 5407, 6959, 7517, 8093, 9341, 10009, 15427, 17191, 21011, 26489, 30089, 32609, 42281, 45293, 51683, 56747, 60251, 73471, 77509, 79561, 90197, 101513, 137209, 142867, 169489, 182047, 191717, 194981, 198301, 201661, 211943

Offset: 1

Author

Daniel Joyce, Oct 01 2014

Keywords

• nonn

Comments

We start with the primes, 2 3 5 7 11 13 17 19 ..., and form the partial sums (starting with the first two terms), 2+3 = 5, ..., but whenever the partial sum is a prime, we remove it from the list of primes to be added later. Thus, 5 will not be added, and the next term in the partial sums is 2+3+7 = 12, and then 2+3+7+11 = 23, which is again prime, thus not used (later) in the partial sum. The primes that are removed are 5, 23, 53, 101, 359, 487, 631, 1669,... and the partial sums are A247658.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A247658.

Cf. A000040, A010051, A007504.

Programs

Haskell

a247657 n = a247657_list !! (n-1)
a247657_list = f 0 $ drop 2 a000040_list where
   f z (p:ps) | a010051' z' == 1 = z' : f z' (delete z' ps)
              | otherwise        = f z' ps
              where z' = z + p
-- Reinhard Zumkeller, Oct 01 2014

PARI

{omit=[];s=2;forprime(p=3,999,if(vecsearch(omit,p),omit=vecextract(omit,"^1");next); isprime(s+=p)||next;print1(s","); omit=concat(omit,s))} \\ M. F. Hasler, Oct 04 2014