A135728 -id:A135728 - cp's OEIS frontend

A135727 Maximal value in orbit of n under the map A001281(x)=3x-1 if x odd, x/2 if x even.

0, 2, 2, 8, 4, 20, 8, 20, 8, 56, 20, 32, 12, 56, 20, 44, 16, 272, 56, 56, 20, 272, 32, 272, 24, 272, 56, 80, 28, 128, 44, 272, 32, 488, 272, 104, 56, 272, 56, 128, 40, 272, 272, 128, 44, 272, 272, 140, 48, 488, 272

Offset: 0

M. F. Hasler, Nov 26 2007

nonn

On the set of positive integers, the orbit of any number under A001281 seems to end in the orbit of 2, of 20 or of 272, which are the respective maxima of these cycles. Since any odd number increases under the map A001281, all elements of this sequence are even.

Cf. A001281, A037084, A039500-A039505, A135728-A135730. A006370, A006577.

A135727(n)=local(m=n);if(n, while( n != 272 & n != 20 & n != 2, if( n%2, n=3*n-1; m=max(n,m), n>>=1)));m

A135729 Record indices of A135727(n)/n = max{ A001281^k(n);k=0,1,2,3... }/n (3x-1 problem).

Original entry on oeis.org

1, 3, 5, 9, 17, 65, 129, 153, 321, 1889, 4097, 10497, 11025, 28161, 149345, 558341, 1467393, 75567105, 299480577, 344371457, 677585217, 788620517, 1951587609, 2672464025, 15958182629, 52002133905, 187559691777, 213121397657

Offset: 1

M. F. Hasler, Nov 26 2007

nonn

This subsequence of A135728 gives indices n for which A135727(n)/n (ratio of maximal value to starting value) is larger than for all preceding indices. Obviously, we cannot consider the index n=0 here.

Cf. A001281, A037084, A039500-A039505, A135727-A135730. A006370, A006577.

A135729(Nmax=10^5)=local(m=0);for(n=1,Nmax,if(m+0A135727(n)/n),print1(n",")))

a(15)-a(28) from Donovan Johnson, Nov 06 2010

cp's OEIS Frontend

A135727 Maximal value in orbit of n under the map A001281(x)=3x-1 if x odd, x/2 if x even.

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