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

1,1

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

Prog

(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

Crossrefs

Cf. A247658.

Cf. A000040, A010051, A007504.

Sequence in context: A135771 A327409 A140811 * A241099 A338977 A090686

Adjacent sequences: A247654 A247655 A247656 * A247658 A247659 A247660

Keyword

nonn

Author

Daniel Joyce, Oct 01 2014

Status

approved