login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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