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A272985
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Numbers n such that the elements of the Collatz trajectory of n are exactly the same as the divisors of n.
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1
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1, 2, 4, 8, 16, 32, 64, 80, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
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OFFSET
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1,2
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COMMENTS
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The number 80 is probably the unique non-power of 2 in the sequence.
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LINKS
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EXAMPLE
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80 is in the sequence because 80 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 with 9 iterations and the divisors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
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MAPLE
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with(numtheory):nn:=10000:
for n from 1 to nn do:
m:=n:it:=0:lst:={n}:
for i from 1 to nn while(m<>1) do:
if irem(m, 2)=0
then
m:=m/2:
else
m:=3*m+1:
fi:
it:=it+1:lst:=lst union {m}:
od:
x:=divisors(n):n0:=nops(x):lst1:={op(x), x[n0]}:
lst2:=lst intersect lst1:n1:=nops(lst2):
if it+1=n1 and n0=n1
then
print(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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