

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

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 A097786 A197649
Adjacent sequences: A109753 A109754 A109755 * A109757 A109758 A109759


KEYWORD

fini,full,nonn


AUTHOR

Werner D. Sand, Aug 12 2005


STATUS

approved



