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Numbers n such that the trajectory of the map n -> (n + lpf(n)) / 2 reaches 3, where lpf(n) is the least prime factor of n (A020639).
1

%I #9 Mar 31 2012 10:22:30

%S 3,4,6,9,10,15,16,18,25,27,28,30,33,34,48,49,51,52,54,55,57,58,63,64,

%T 66,91,93,94,96,99,100,102,105,106,108,111,112,114,119,121,123,124,

%U 126,129,130,169,180,183,184,186,187,189,190,195,196,198

%N Numbers n such that the trajectory of the map n -> (n + lpf(n)) / 2 reaches 3, where lpf(n) is the least prime factor of n (A020639).

%C The only prime term is 3 because all primes map to themselves.

%e (15 + 3) / 2 = 9, (9 + 3) / 2 = 6, (6 + 2) / 2 = 4, and (4 + 2) / 2 = 3, thus 15 is in the sequence.

%e (21 + 3) / 2 = 12, (12 + 2) / 2 = 7, and (7 + 7) / 2 = 7, so 21 never reaches 3 and therefore is not in the sequence.

%Y Cf. A177980, A020639, A061228.

%K nonn

%O 1,1

%A _Grant Garcia_, Jan 06 2011