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.

7, 31, 109, 349, 1061, 103, 29, 97, 43, 13, 11, 41, 131, 37, 17, 59

Offset: 1

Author

Werner D. Sand, Aug 12 2005

Keywords

• fini
• full
• nonn

Comments

You can invent numerous variations which generate other cycles, but always you end in 2 or 3 cycles.

Examples

			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.

Formula

p+q+r=s, prime. s=p. repeat. p+q+r=s=f1*f2*f3..., fi prime. Largest f=p. repeat.