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 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. 2
 7, 31, 109, 349, 1061, 103, 29, 97, 43, 13, 11, 41, 131, 37, 17, 59 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS You can invent numerous variations which generate other cycles, but always you end in 2 or 3 cycles. LINKS FORMULA p+q+r=s, prime. s=p. repeat. p+q+r=s=f1*f2*f3..., fi prime. Largest f=p. repeat. EXAMPLE p=7 7+11+13=31 31+37+41=109 109+113+127=349 349+353+359=1061 1061+1063+1069=3193=31*103 103+107+109=319=11*29 29+31+37=97 97+101+103=301=7*43 43+47+53=143=11*13 13+17+19=49=7*7 7+11+13... CROSSREFS Cf. A117631. Sequence in context: A055366 A160607 A205492 * A055580 A097786 A197649 Adjacent sequences:  A109753 A109754 A109755 * A109757 A109758 A109759 KEYWORD fini,full,nonn AUTHOR Werner D. Sand, Aug 12 2005 STATUS approved

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Last modified October 21 04:12 EDT 2018. Contains 316405 sequences. (Running on oeis4.)