A281665 Numbers m such that A006667(m)/A006577(m) = 1/3.

159, 283, 377, 502, 503, 603, 615, 668, 669, 670, 799, 807, 888, 890, 892, 893, 1063, 1065, 1095, 1186, 1187, 1188, 1189, 1190, 1417, 1435, 1580, 1581, 1582, 1585, 1586, 1587, 1889, 1913, 1947, 1959, 1963, 2104, 2106, 2108, 2109, 2113, 2114, 2115, 2119, 2518

Offset: 1

Author

Michel Lagneau, Jan 31 2017

Keywords

• nonn

Comments

A006667: number of tripling steps to reach 1 in '3x+1' problem.

A006577: number of halving and tripling steps to reach 1 in '3x+1' problem.

The corresponding number of iterations A006577(a(n)) is given by the sequence 54, 60, 63, 66, 66, 69, 69, 69, 69, 69, 72, 72, 72, 72, 72, 72, 75, 75, ... and the set of the distinct values of this sequence is {b(n)} = {54, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, ...}. We observe that {b(k)} = {54} union {60 + 3*k} for k = 1, 2, ...

Examples

			159 is in the sequence because A006667(159)/A006577(159) = 18/54 = 1/3.
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006577, A006666, A006667.

Programs

Maple

nn:=10000:
for n from 2 to 3000 do:
  m:=n:s1:=0:s2:=0:
   for i from 1 to nn while(m<>1) do:
    if irem(m,2)=0
     then
     s2:=s2+1:m:=m/2:
     else
     s1:=s1+1:m:=3*m+1:
    fi:
   od:
   s:=s1/(s1+s2):
    if s=1/3
     then
     printf(`%d, `,n):
     else
    fi:
od: