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

1,1

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, ...

Links

Table of n, a(n) for n=1..46.

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

Example

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

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:

Crossrefs

Cf. A006577, A006666, A006667.

Sequence in context: A192173 A093472 A270304 * A329535 A250659 A280971

Adjacent sequences: A281662 A281663 A281664 * A281666 A281667 A281668

Keyword

nonn

Author

Michel Lagneau, Jan 31 2017

Status

approved