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

1,1

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

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

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 *)

Crossrefs

From the third term onwards the sequence coincides with A076272.

Sequence in context: A029160 A285582 A032562 * A337931 A008649 A008650

Adjacent sequences: A076970 A076971 A076972 * A076974 A076975 A076976

Keyword

nonn

Author

Amarnath Murthy, Oct 22 2002

Extensions

More terms from Sascha Kurz, Jan 22 2003

Status

approved