A317083 a(n) is the first term less than the initial 2n+1 in the reduced Collatz trajectory.

1, 1, 1, 5, 7, 5, 5, 5, 13, 11, 1, 5, 19, 23, 11, 23, 25, 5, 7, 19, 31, 37, 17, 23, 37, 29, 5, 47, 43, 19, 23, 61, 49, 19, 13, 61, 55, 1, 29, 19, 61, 47, 1, 37, 67, 61, 35, 91, 73, 7, 19, 61, 79, 91, 41, 61, 85, 65, 11, 101, 91, 59, 47, 77, 97, 37, 25, 43, 103

Offset: 0

Author

Michel Lagneau, Jul 21 2018

Keywords

• nonn

Examples

			a(3)= 5 because, starting with 7, the iteration produces 11,17,13,5 and 5 is the first term less than 7.
		

Crossrefs

Cf. A122458, A256598.

Programs

Mathematica

f[n_]:=NestWhileList[(3*#+1)/2^IntegerExponent[3*#+1,2]&,2*n+1,#>1&];
nextOddK[n_]:=Module[{m=3n+1},While[EvenQ[m],m=m/2];m];dt[n_]:=Module[{m=n,cnt=0},If[n>1,While[m=nextOddK[m];cnt++;m>n]];cnt];
Table[Part[f[i],dt[2i+1]+1],{i,0,70}]