A180101 a(0)=0, a(1)=1; thereafter a(n) = largest prime factor of sum of all previous terms.

0, 1, 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41

Offset: 0

Author

N. J. A. Sloane, Jan 16 2011

Keywords

• nonn

Comments

More precisely, a(n) = A006530 applied to sum of previous terms.

Inspired by A175723.

Except for initial terms, same as A076272, but the simple definition warrants an independent entry.

Crossrefs

Cf. A006530, A076272, A175723, A180107 (partial sums).

Formula

For the purposes of this paragraph, regard 0 as the (-1)st prime and 1 as the 0th prime. Conjectures: All primes appear; the primes appear in increasing order; the k-th prime p(k) appears p(k+1)-p(k-1) times (cf. A031131); and p(k) appears for the first time at position A164653(k) (sums of two consecutive primes). These assertions are stated as conjectures only because I have not written out a formal proof, but they are surely true.