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

0,4

Links

Table of n, a(n) for n=0..68.

Example

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

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}]

Crossrefs

Cf. A122458, A256598.

Sequence in context: A104542 A161376 A107437 * A367549 A122271 A011205

Adjacent sequences: A317080 A317081 A317082 * A317084 A317085 A317086

Keyword

nonn

Author

Michel Lagneau, Jul 21 2018

Status

approved