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A076973 Starting with 2, largest prime divisor of the sum of all previous terms. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 03:32 EST 2023. Contains 359939 sequences. (Running on oeis4.)