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

0,4

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.

Links

Table of n, a(n) for n=0..81.

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.

Crossrefs

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

Sequence in context: A130312 A295629 A076272 * A108035 A202503 A049747

Adjacent sequences: A180098 A180099 A180100 * A180102 A180103 A180104

Keyword

nonn

Author

N. J. A. Sloane, Jan 16 2011

Status

approved