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A174539
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Starting numbers n such that the number of halving and tripling steps to reach 1 under the Collatz 3x+1 map is a perfect square.
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0
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1, 2, 7, 12, 13, 16, 44, 45, 46, 80, 84, 85, 98, 99, 100, 101, 102, 107, 129, 153, 156, 157, 158, 169, 272, 276, 277, 280, 282, 300, 301, 302, 350, 351, 512, 576, 592, 608, 616, 618, 625, 642, 643, 644, 645, 646, 648, 649, 650, 651, 652, 653, 654, 655, 662, 663
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OFFSET
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1,2
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COMMENTS
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Numbers n such that A006577(n) is a perfect square.
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LINKS
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Table of n, a(n) for n=1..56.
Index to sequences related to the 3x+1 problem
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FORMULA
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{n: A006577(n) in A000290}.
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EXAMPLE
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44, 45 and 46 are in the sequence because the number of steps as counted in A006577 for each of them is 16 = 4^2, a perfect square.
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MAPLE
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with(numtheory):for x from 1 to 200 do traj:=0: n1:=x: x1:=x: for p from 1 to 20 while(irem(x1, 2)=0)do p1:=2^p: xx1:=x1: x1:=floor(n1/p1): traj:=traj+1:od:
n:=x1: for q from 1 to 100 while(n<>1)do n1:=3*n+1: traj:=traj+1: x0:=irem(n1, 2): for p from 1 to 20 while(x0=0)do p1:=2^p: xx1:=x1: x1:=floor(n1/p1): x0:=n1-p1*x1: traj:=traj+1: od: traj:=traj-1: n:=xx1:od:
if(sqrt(traj))=floor(sqrt(traj)) then print(x):else fi:od:
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CROSSREFS
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Cf. A006577, A008908, A064433, A006666, A006667, A033491
Sequence in context: A064441 A110949 A126343 * A049409 A190548 A187971
Adjacent sequences: A174536 A174537 A174538 * A174540 A174541 A174542
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KEYWORD
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nonn
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AUTHOR
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Michel Lagneau, Mar 21 2010
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EXTENSIONS
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Unspecific references removed - R. J. Mathar, Mar 31 2010
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STATUS
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approved
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