A076973 Starting with 2, largest prime divisor of the sum of all previous terms.

2, 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

Offset: 1

Author

Amarnath Murthy, Oct 22 2002

Keywords

• nonn

Comments

Conjecture: start from any initial value a(1) = m >= 2 and define a(n) to be the largest prime factor of a(1)+a(2)+...+a(n-1); then a(n) = n/2 + O(log(n)) and there are infinitely many primes p such that a(2p)=p. - Benoit Cloitre, Jun 04 2003

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

From the third term onwards the sequence coincides with A076272.

Programs

Mathematica

nxt[{t_,a_}]:=Module[{c=FactorInteger[t][[-1,1]]},{t+c,c}]; NestList[nxt,{2,2},80][[All,2]] (* Harvey P. Dale, May 21 2017 *)

Formula

a(n) = p(m) (the m-th prime), where m is the smallest index such that n <= p(m+1) + p(m) - 2. - Max Alekseyev, Oct 21 2008

Extensions

More terms from Sascha Kurz, Jan 22 2003