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 A180101 a(0)=0, a(1)=1; thereafter a(n) = largest prime factor of sum of all previous terms. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified February 25 04:32 EST 2020. Contains 332217 sequences. (Running on oeis4.)