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A225570
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The greedy smallest infinite reverse Collatz (3x+1) sequence.
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2
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1, 2, 4, 8, 16, 5, 10, 20, 40, 13, 26, 52, 17, 34, 11, 22, 7, 14, 28, 56, 112, 37, 74, 148, 49, 98, 196, 65, 130, 43, 86, 172, 344, 688, 229, 458, 916, 305, 610, 203, 406, 812, 1624, 541, 1082, 2164, 721, 1442, 2884, 961, 1922, 3844, 7688, 15376, 5125, 10250
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OFFSET
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1,2
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COMMENTS
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For each a(n) (where n > 4), a(n) = (a(n-1) - 1)/3 if the result is an odd integer not divisible by 3. Otherwise a(n) = 2 * a(n-1).
Going backwards from any term a(n) to a(1), this is the Collatz sequence for a(n). Furthermore, each term in the sequence is the smallest possible term (ignoring multiples of 3) with this property given the previous term.
Multiples of 3 are ignored because after visiting a multiple of 3, subsequent terms can only double.
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LINKS
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MAPLE
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local a;
option remember;
if n <= 4 then
2^(n-1) ;
else
a := (procname(n-1)-1)/3 ;
if type(a, 'integer') and type(a, 'odd') and modp(a, 3) <> 0 then
return a;
else
return procname(n-1)*2 ;
end if;
end if;
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MATHEMATICA
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last = 8; Join[{1, 2, 4, 8}, Table[test = (last - 1)/3; If[OddQ[last] || ! IntegerQ[test] || IntegerQ[test/3], last = 2*last, last = (last - 1)/3]; last, {96}]] (* T. D. Noe, Aug 11 2013 *)
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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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