

A117631


a(1)=433640083; a(n+1)= the largest prime factor of a(n)+b(n)+c(n), where a(n)<b(n)<c(n) and a(n),b(n) and c(n) are three consecutive primes.


1



433640083, 1300920277, 3902760919, 1300920311, 3902760991, 285567881, 19923341, 59770063, 432073, 432097, 259271, 777857, 2333579, 72173, 43321, 130043, 390151, 40361, 121171, 363541, 4211, 12647, 12653, 1151, 3467, 10427, 467
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OFFSET

1,1


COMMENTS

Note that before entering the cycle (41, 131, 37, 11) there are 34 terms of the sequence a(1),a(2),...,a(33)=53 and a(34)=173.


LINKS

Table of n, a(n) for n=1..27.
Carlos Rivera, Puzzle 354.


FORMULA

If k is a natural number then a(4k+31)=41; a(4k+32)=131; a(4k+33)=37 and a(4k+34)=11.


EXAMPLE

a(1)=433640083 so b(1)=nextprime(433640083)=433640093 and c(1)=nextprime(433640093)=433640101 hence a(2) equals largest prime factor of 433640083+433640093+433640101.
But 433640083+433640093+433640101=1300920277 is prime so a(2)= 1300920277.


MATHEMATICA

np[n_]:=Module[{np1=NextPrime[n], np2}, np2=NextPrime[np1]; Max[Transpose[ FactorInteger[n+np1+np2]]]]; NestList[np, 433640083, 50] (* Harvey P. Dale, Sep 22 2011 *)


CROSSREFS

Cf. A109756.
Sequence in context: A017528 A283872 A233477 * A022229 A022260 A209210
Adjacent sequences: A117628 A117629 A117630 * A117632 A117633 A117634


KEYWORD

easy,nonn


AUTHOR

Enoch Haga and Farideh Firoozbakht, Apr 08 2006


STATUS

approved



