A082021 -id:A082021 - cp's OEIS frontend

A082132 a(0) = 5; for n > 0, a(n) is the greatest prime factor of PP(a(n-1))*a(n-1)-2 where PP(n) is an abbreviation for PreviousPrime(n).

5, 13, 47, 673, 1093, 4789, 15887, 6961, 7079, 1853387, 5636791, 16319158451, 46975091221, 97536826417, 9513432505744326182381, 2335222008886384800739, 7440517660385876970522347503153, 83914607657246408236765553419, 1960358081272210906656999086971746456168551

Offset: 0

Yasutoshi Kohmoto, May 10 2003

nonn

Some of the larger entries may only correspond to probable primes.

Tyler Busby, Table of n, a(n) for n = 0..22

Cf. A082021, A031441, A031442.

p=5;for(k=1,20,print1(p,",");p=precprime(p-1)*p-2;f=factor(p);s=matsize(f)[1];p=f[s,1]) \\ Rick L. Shepherd, Dec 19 2004

Edited by Rick L. Shepherd, Dec 19 2004

a(18) from Tyler Busby, Oct 22 2023

A083557 a(n) is the greatest prime factor of 3*a(n-1)+2.

Original entry on oeis.org

3, 11, 7, 23, 71, 43, 131, 79, 239, 719, 127, 383, 1151, 691, 83, 251, 151, 13, 41, 5, 17, 53, 23, 71, 43, 131, 79, 239, 719, 127, 383, 1151, 691, 83, 251, 151, 13, 41, 5, 17, 53, 23, 71, 43, 131, 79, 239, 719, 127, 383, 1151, 691, 83, 251, 151, 13, 41, 5, 17, 53, 23

Offset: 1

Yasutoshi Kohmoto, Jun 05 2003

nonn

Conjecture: if a(1)=m then the sequence becomes cyclic, for any m.

Conjecture verified up to 25000000 by Jud McCranie, Jun 11 2003

Cf. A031439, A031440, A031442, A082021, A082132, A084923.

f[n_] := Flatten[Table[ #[[1]], {1}] & /@ FactorInteger[ 3n + 2 ]][[ -1]]; NestWhileList[f, 3, UnsameQ, All]
NestList[FactorInteger[3#+2][[-1,1]]&,3,70] (* Harvey P. Dale, Feb 21 2013 *)

lista(nn) = {print1(a = 3, ", "); for (n=1, nn, a = vecmax(factor(3*a+2)[,1]); print1(a, ", "););} \\ Michel Marcus, Jul 15 2017

G.f.: x*(3 + 11*x + 7*x^2 + 23*x^3 + 71*x^4 + 43*x^5 + 131*x^6 + 79*x^7 + 239*x^8 + 719*x^9 + 127*x^10 + 383*x^11 + 1151*x^12 + 691*x^13 + 83*x^14 + 251*x^15 + 151*x^16 + 13*x^17 + 41*x^18 + 2*x^19 + 6*x^20 + 46*x^21) / (1 - x^19) (conjectured). - Colin Barker, Jul 15 2017

cp's OEIS Frontend

A082132 a(0) = 5; for n > 0, a(n) is the greatest prime factor of PP(a(n-1))*a(n-1)-2 where PP(n) is an abbreviation for PreviousPrime(n).

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