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Starting with n (but omitting the primes), repeatedly sum prime factors (counted with multiplicity) until reaching a limit.
3

%I #13 Oct 12 2013 15:29:00

%S 0,4,5,5,5,7,7,5,5,5,5,5,7,13,5,7,5,5,11,7,7,5,19,7,7,7,5,11,7,5,11,7,

%T 11,5,7,5,17,11,5,13,13,31,7,5,13,7,5,5,7,5,5,7,5,13,23,5,5,13,7,43,5,

%U 13,11,7,17,13,5,5,19,5,5,13,5,17,5,13,19,5,5,13,5,11,5,5,11,5

%N Starting with n (but omitting the primes), repeatedly sum prime factors (counted with multiplicity) until reaching a limit.

%C Is this sequence generating ALL prime numbers (greater than 3) ? Also how many times each prime (greater than 3)is generated in this sequence? [From _Alexander R. Povolotsky_, Nov 05 2008]

%H Paolo P. Lava, <a href="/A029909/b029909.txt">Table of n, a(n) for n = 1..10000</a>

%e 20 -> 2+2+5 = 9 -> 3+3 = 6 -> 2+3 = 5.

%Y Cf. A029908.

%K nonn

%O 1,2

%A _Dann Toliver_