A303811 Least k such that A006666(k)/A006667(k) = prime(n).

159, 6, 10, 40, 640, 2560, 40960, 163840, 2621440, 167772160, 671088640, 42949672960, 687194767360, 2748779069440, 43980465111040, 2814749767106560, 180143985094819840, 720575940379279360, 46116860184273879040, 737869762948382064640, 2951479051793528258560

Offset: 1

Author

Michel Lagneau, Sep 10 2018

Keywords

• nonn

Comments

A006666 and A006667 are respectively the number of halving and tripling steps in the '3x+1' problem.

For n > 2, it seems that a(n) is of the form a(n) = 5*2^q with q = 1, 3, 7, 9, 13, 15, 19, 25, 27, 33, 37, 39, 43, 49, 55, 57, 63, 67, 69, ... (Numbers q such that q+4 is prime: A172367)

Examples

			a(4) = 40 because A006666(40)/A006667(40) = 7/1 = prime(4).
		

Crossrefs

Cf. A006577, A006666, A006667, A172367, A287798.

Programs

Maple

nn:=10^20:
for n from 1 to 10 do:
ii:=0:
   for k from 1 to nn while(ii=0) do:
    it0:=0:it1:=0:m:=k:
      for i from 1 to nn while(m<>1) do:
        if irem(m, 2)=0
         then
         m:=m/2:it0:=it0+1:
         else
         m:=3*m+1:it1:=it1+1:
       fi:
     od:
      if it1<>0 and it0/it1 = ithprime(n)
       then
       ii:=1:printf(`%d %d \n`,n,k):
       else
     fi:
od:
od: