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 A281665 Numbers m such that A006667(m)/A006577(m) = 1/3. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 28 19:54 EDT 2020. Contains 333103 sequences. (Running on oeis4.)