cp's OEIS Frontend

A109756 If you sum 3 consecutive odd prime numbers p,q,r, you get a number s which is either prime or not: p+q+r=s. If s is prime, you call it p and repeat the game. If s is not prime, you call the largest prime factor p and repeat the game. Finally, you get into an infinite cycle, which is one of the above 3 sequences, no matter what initial prime numbers you choose.

%I A109756 #7 Feb 18 2015 02:25:17
%S A109756 7,31,109,349,1061,103,29,97,43,13,11,41,131,37,17,59
%N A109756 If you sum 3 consecutive odd prime numbers p,q,r, you get a number s which is either prime or not: p+q+r=s. If s is prime, you call it p and repeat the game. If s is not prime, you call the largest prime factor p and repeat the game. Finally, you get into an infinite cycle, which is one of the above 3 sequences, no matter what initial prime numbers you choose.
%C A109756 You can invent numerous variations which generate other cycles, but always you end in 2 or 3 cycles.
%F A109756 p+q+r=s, prime. s=p. repeat. p+q+r=s=f1*f2*f3..., fi prime. Largest f=p. repeat.
%e A109756 p=7
%e A109756 7+11+13=31
%e A109756 31+37+41=109
%e A109756 109+113+127=349
%e A109756 349+353+359=1061
%e A109756 1061+1063+1069=3193=31*103
%e A109756 103+107+109=319=11*29
%e A109756 29+31+37=97
%e A109756 97+101+103=301=7*43
%e A109756 43+47+53=143=11*13
%e A109756 13+17+19=49=7*7
%e A109756 7+11+13...
%Y A109756 Cf. A117631.
%K A109756 fini,full,nonn
%O A109756 1,1
%A A109756 _Werner D. Sand_, Aug 12 2005