cp's OEIS Frontend

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

%I A023525 #32 Aug 14 2015 17:10:16
%S A023525 3,7,2,3,13,3,37,3,73,167,5,41,23,7,337,89,23,5,73,61,3,103,1093,1847,
%T A023525 1439,71,17,167,3,2053,23,59,641,23,863,5,5927,457,349,233,79,5,67,3,
%U A023525 6337,11,19,3361,59,19,8893,6961,5,71,16127,71,769,5,383
%N A023525 Greatest prime divisor of prime(n)*prime(n-1) + 1.
%C A023525 This sequence assumes prime(0) = 1.
%C A023525 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
%H A023525 Harvey P. Dale and Robert Israel, <a href="/A023525/b023525.txt">Table of n, a(n) for n = 1..10000</a>(1..1000 from Harvey P. Dale)
%F A023525 a(n) = A006530(A023523(n)). - _Michel Marcus_, Aug 12 2015
%p A023525 Primes:= select(isprime,[2,(2*i+1 $ i=1..1000)]):
%p A023525 3, seq(max(numtheory:-factorset(Primes[i]*Primes[i+1]+1)), i=1..nops(Primes)-1); # _Robert Israel_, Aug 14 2015
%t A023525 Join[{3},FactorInteger[#][[-1,1]]&/@(Times@@@Partition[Prime[ Range[ 60]], 2,1]+1)] (* _Harvey P. Dale_, Apr 12 2013 *)
%o A023525 (PARI) gpf(n)=my(f=factor(n)[, 1]~);f[#f];
%o A023525 myprime(n)=if(n==0,1,prime(n));
%o A023525 first(m)=vector(m,i,gpf(1+myprime(i)*myprime(i-1))); \\ _Anders Hellström_, Aug 13 2015
%Y A023525 Cf. A006530, A023523.
%K A023525 nonn
%O A023525 1,1
%A A023525 _Clark Kimberling_