A109756 -id:A109756 - cp's OEIS frontend

A117631 a(1)=433640083; a(n+1)= the largest prime factor of a(n)+b(n)+c(n), where a(n)

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

Enoch Haga and Farideh Firoozbakht, Apr 08 2006

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.

			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.

Carlos Rivera, Puzzle 354.

Cf. A109756.

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 *)

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

A117675 Numbers k such that prime(k) + prime(k+1) + prime(k+2) is prime and also there is a j such that prime(j) + prime(j+1) + prime(j+2) = prime(k).

Original entry on oeis.org

9, 11, 13, 20, 23, 29, 47, 64, 70, 88, 121, 126, 145, 148, 153, 174, 190, 195, 201, 213, 223, 245, 294, 298, 320, 337, 369, 381, 429, 436, 445, 462, 486, 495, 504, 536, 548, 584, 596, 608, 639, 677, 747, 819, 827, 831, 868, 877, 887, 902, 905, 970

Offset: 1

Roger L. Bagula, Apr 12 2006

nonn

Cf. A109756, A072225.

isok2(k)={my(q=prime(k), p=q\3); while(p>2, p=precprime(p-1); my(p2=nextprime(p+1), t=p+p2+nextprime(p2+1)); if(t<=q, return(t==q))); 0}
isok(k)={my(p1=prime(k), p2=nextprime(p1+1), p3=nextprime(p2+1)); isprime(p1+p2+p3) && isok2(k)}
select(isok, [1..1000]) \\ Andrew Howroyd, Jul 23 2024

Edited and more terms from Andrew Howroyd, Jul 23 2024

cp's OEIS Frontend

A117631 a(1)=433640083; a(n+1)= the largest prime factor of a(n)+b(n)+c(n), where a(n)

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