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A109756
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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.
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2
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7, 31, 109, 349, 1061, 103, 29, 97, 43, 13, 11, 41, 131, 37, 17, 59
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| You can invent numerous variations which generate other cycles, but always you end in 2 or 3 cycles.
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FORMULA
| p+q+r=s, prime. s=p. repeat. p+q+r=s=f1*f2*f3..., fi prime. Largest f=p. repeat.
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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...
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CROSSREFS
| Compare A117631.
Sequence in context: A055366 A160607 A205492 * A055580 A097786 A197649
Adjacent sequences: A109753 A109754 A109755 * A109757 A109758 A109759
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KEYWORD
| fini,full,nonn
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AUTHOR
| Werner Dietrich Sand (Werner.Sand(AT)web.de), Aug 12 2005
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