A023525 Greatest prime divisor of prime(n)*prime(n-1) + 1.

3, 7, 2, 3, 13, 3, 37, 3, 73, 167, 5, 41, 23, 7, 337, 89, 23, 5, 73, 61, 3, 103, 1093, 1847, 1439, 71, 17, 167, 3, 2053, 23, 59, 641, 23, 863, 5, 5927, 457, 349, 233, 79, 5, 67, 3, 6337, 11, 19, 3361, 59, 19, 8893, 6961, 5, 71, 16127, 71, 769, 5, 383

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

This sequence assumes prime(0) = 1.

Heuristically, we should expect a(n) -> infinity as n -> infinity, i.e. for any k there should be only finitely many terms <= k. It seems likely that 3 is the only n for which a(n) = 2. There are at least 14 occurrences of a(n) = 3, including 1, 4, 6, 8, 21, 29, 44, 84, 191, 378, 13006, 39420, 62947, 78156. - Robert Israel, Aug 14 2015

Links

• Harvey P. Dale and Robert Israel, Table of n, a(n) for n = 1..10000(1..1000 from Harvey P. Dale)

Crossrefs

Cf. A006530, A023523.

Programs

Maple

Primes:= select(isprime,[2,(2*i+1 $ i=1..1000)]):
3, seq(max(numtheory:-factorset(Primes[i]*Primes[i+1]+1)), i=1..nops(Primes)-1); # Robert Israel, Aug 14 2015

Mathematica

Join[{3},FactorInteger[#][[-1,1]]&/@(Times@@@Partition[Prime[ Range[ 60]], 2,1]+1)] (* Harvey P. Dale, Apr 12 2013 *)

PARI

gpf(n)=my(f=factor(n)[, 1]~);f[#f];
myprime(n)=if(n==0,1,prime(n));
first(m)=vector(m,i,gpf(1+myprime(i)*myprime(i-1))); \\ Anders Hellström, Aug 13 2015

Formula

a(n) = A006530(A023523(n)). - Michel Marcus, Aug 12 2015