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.

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

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