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A056959
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In repeated iterations of function m -> m/2 if m even, m -> 3m+1 if m odd, a(n) is maximum value achieved if starting from n.
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3
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4, 4, 16, 4, 16, 16, 52, 8, 52, 16, 52, 16, 40, 52, 160, 16, 52, 52, 88, 20, 64, 52, 160, 24, 88, 40, 9232, 52, 88, 160, 9232, 32, 100, 52, 160, 52, 112, 88, 304, 40, 9232, 64, 196, 52, 136, 160, 9232, 48, 148, 88, 232, 52, 160, 9232, 9232, 56, 196, 88, 304, 160, 184
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OFFSET
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1,1
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COMMENTS
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If a(n) exists (which is the essence of the "3x+1" problem) then a(n) must be a multiple of 4, since if a(n) was odd then the next iteration 3*a(n)+1 would be greater than a(n), while if a(n) was twice an odd number then the next-but-one iteration (3/2)*a(n)+1 would be greater.
The variant A025586 considers the trajectory ending in 1, by definition. Therefore the two sequences differ for a(1) and a(2). - M. F. Hasler, Oct 20 2019
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LINKS
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Table of n, a(n) for n=1..61.
Index entries for sequences related to 3x+1 (or Collatz) problem
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EXAMPLE
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a(6)=16 since iteration starts: 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... and 16 is highest value
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PROG
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(PARI) a(n)=my(r=max(4, n)); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n), n/=2)); r \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
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Cf. A006370, A056957, A056958.
Essentially the same as A025586.
Sequence in context: A177241 A076821 A165825 * A255300 A255298 A255302
Adjacent sequences: A056956 A056957 A056958 * A056960 A056961 A056962
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley, Jul 18 2000
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STATUS
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approved
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