cp's OEIS Frontend

A224693 Smallest prime p such that p > gpf(p+1) > gpf(p+2) > ... > gpf(p+n) where gpf(m) is the greatest prime factor of m.

%I A224693 #20 Sep 15 2017 13:44:27
%S A224693 3,13,13,491,2011,12721,12721,109453,586951,173912393,785211341,
%T A224693 4044619541,315400191511,315400191511
%N A224693 Smallest prime p such that p > gpf(p+1) > gpf(p+2) > ... > gpf(p+n) where gpf(m) is the greatest prime factor of m.
%C A224693 a(n) >= A100385(n+1). - _Zak Seidov_, Apr 17 2013
%e A224693 a(4) = 491 because 491 > 41 > 29 > 19 > 11 where:
%e A224693 492 = 2^2*3*41;
%e A224693 493 = 17*29;
%e A224693 494 = 2*13*19;
%e A224693 495 = 3^2*5*11.
%p A224693 with(numtheory):
%p A224693 for n from 1 to 20 do:
%p A224693    ii:=0:
%p A224693         for k from 1 to 10^7 while(ii=0) do:
%p A224693         p:=ithprime(k): it:=0:
%p A224693             for m from 1 to n do:
%p A224693                x0:=factorset(p+m-1):n0:=nops(x0): x1:=factorset(p+m):n1:=nops(x1):
%p A224693                if x0[n0] > x1[n1]
%p A224693                then
%p A224693                it:=it+1:
%p A224693               else
%p A224693               fi:
%p A224693           od:
%p A224693              if it=n
%p A224693              then
%p A224693              printf ( "%d %d \n",n,p):ii:=1:
%p A224693              else
%p A224693              fi:
%p A224693         od:
%p A224693     od:
%Y A224693 Cf. A006530, A100385.
%K A224693 nonn,hard,more
%O A224693 1,1
%A A224693 _Michel Lagneau_, Apr 15 2013
%E A224693 a(10)-a(12) from _Zak Seidov_, Apr 17 2013
%E A224693 a(13)-a(14) from _Donovan Johnson_, Apr 26 2013