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.

3, 13, 13, 491, 2011, 12721, 12721, 109453, 586951, 173912393, 785211341, 4044619541, 315400191511, 315400191511

Offset: 1

Author

Michel Lagneau, Apr 15 2013

Keywords

• nonn
• hard
• more

Comments

a(n) >= A100385(n+1). - Zak Seidov, Apr 17 2013

Examples

			a(4) = 491 because 491 > 41 > 29 > 19 > 11 where:
492 = 2^2*3*41;
493 = 17*29;
494 = 2*13*19;
495 = 3^2*5*11.
		

Crossrefs

Cf. A006530, A100385.

Programs

Maple

with(numtheory):
for n from 1 to 20 do:
   ii:=0:
        for k from 1 to 10^7 while(ii=0) do:
        p:=ithprime(k): it:=0:
            for m from 1 to n do:
               x0:=factorset(p+m-1):n0:=nops(x0): x1:=factorset(p+m):n1:=nops(x1):
               if x0[n0] > x1[n1]
               then
               it:=it+1:
              else
              fi:
          od:
             if it=n
             then
             printf ( "%d %d \n",n,p):ii:=1:
             else
             fi:
        od:
    od:

Extensions

a(10)-a(12) from Zak Seidov, Apr 17 2013

a(13)-a(14) from Donovan Johnson, Apr 26 2013