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

Author

Omar E. Pol, Sep 09 2021

Keywords

• nonn

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.

Examples

			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).
		

Links

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

Crossrefs

Records in A235795.

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

Programs

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

Extensions

More terms from Michel Marcus, Sep 10 2021