A347652 Records in the trajectory of all positive integers in the 3x+1 or Collatz problem, including the trajectory [1, 4, 2, 1] of 1.

1, 4, 10, 16, 22, 34, 52, 70, 106, 160, 214, 322, 484, 700, 790, 1186, 1780, 2158, 3238, 4858, 7288, 9232, 13120, 17224, 17494, 26242, 39364, 41524, 45682, 68524, 77092, 97576, 98962, 148444, 167002, 250504, 354292, 504466, 756700, 851290, 1276936, 1417174, 2125762

Offset

1,2

Comments

Replacing the second term (4) with the first two primes (2, 3) we have 1, 2, 3, 10, 16, 22, ... the records in A070165.

Links

Table of n, a(n) for n=1..43.

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

The first three rows of A235795 are [1, 4, 2, 1]; [2, 1]; [3, 10, 5, 16, 8, 4, 2, 1]. The records are [1, 4, 10, 16], the same as a(1)..a(4).

Prog

(PARI) f(n) = if (n%2, 3*n+1, n/2); \\ A014682
row(n) = {my(list=List()); listput(list, n); until(n==1, n = f(n); listput(list, n)); Vec(list); } \\ A235795
lista(nn) = {my(m=0, list = List()); for (n=1, nn, my(v = row(n)); for (k=1, #v, if (v[k]>m, m=v[k]; listput(list, m); ); )); Vec(list); } \\ Michel Marcus, Sep 10 2021

Crossrefs

Records in A235795.

Cf. A006370, A070165, A235800, A347270 (all 3x+1 sequences).

Sequence in context: A294636 A295560 A161644 * A215032 A294980 A310534

Adjacent sequences: A347649 A347650 A347651 * A347653 A347654 A347655

Keyword

nonn

Author

Omar E. Pol, Sep 09 2021

Extensions

More terms from Michel Marcus, Sep 10 2021

Status

approved