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

%I A303811 #21 Sep 15 2018 15:51:45
%S A303811 159,6,10,40,640,2560,40960,163840,2621440,167772160,671088640,
%T A303811 42949672960,687194767360,2748779069440,43980465111040,
%U A303811 2814749767106560,180143985094819840,720575940379279360,46116860184273879040,737869762948382064640,2951479051793528258560
%N A303811 Least k such that A006666(k)/A006667(k) = prime(n).
%C A303811 A006666 and A006667 are respectively the number of halving and tripling steps in the '3x+1' problem.
%C A303811 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)
%e A303811 a(4) = 40 because A006666(40)/A006667(40) = 7/1 = prime(4).
%p A303811 nn:=10^20:
%p A303811 for n from 1 to 10 do:
%p A303811 ii:=0:
%p A303811    for k from 1 to nn while(ii=0) do:
%p A303811     it0:=0:it1:=0:m:=k:
%p A303811       for i from 1 to nn while(m<>1) do:
%p A303811         if irem(m, 2)=0
%p A303811          then
%p A303811          m:=m/2:it0:=it0+1:
%p A303811          else
%p A303811          m:=3*m+1:it1:=it1+1:
%p A303811        fi:
%p A303811      od:
%p A303811       if it1<>0 and it0/it1 = ithprime(n)
%p A303811        then
%p A303811        ii:=1:printf(`%d %d \n`,n,k):
%p A303811        else
%p A303811      fi:
%p A303811 od:
%p A303811 od:
%Y A303811 Cf. A006577, A006666, A006667, A172367, A287798.
%K A303811 nonn
%O A303811 1,1
%A A303811 _Michel Lagneau_, Sep 10 2018