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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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159 is in the sequence because A006667(159)/A006577(159) = 18/54 = 1/3.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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