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

1,1

Comments

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

Links

Table of n, a(n) for n=1..16.

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 A364635 A097786

Adjacent sequences: A109753 A109754 A109755 * A109757 A109758 A109759

Keyword

fini,full,nonn

Author

Werner D. Sand, Aug 12 2005

Status

approved