A060565 Follow trajectory of 2n+1 in the '3x+1' problem until a lower number is reached; A060445 gives number of steps for this to happen. Sequence gives the first lower number that is reached.

2, 4, 5, 7, 10, 10, 10, 13, 11, 16, 20, 19, 23, 22, 23, 25, 20, 28, 38, 31, 37, 34, 46, 37, 29, 40, 47, 43, 38, 46, 61, 49, 38, 52, 61, 55, 64, 58, 76, 61, 47, 64, 74, 67, 61, 70, 91, 73, 56, 76, 61, 79, 91, 82, 61, 85, 65, 88, 101, 91, 118, 94, 77, 97, 74, 100, 86, 103

Offset: 1

Author

N. J. A. Sloane, Apr 12 2001

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A060445.

Programs

Maple

b:= proc(n, t) option remember; `if`(n b((2*n+1)$2):
seq(a(n), n=1..80);  # Alois P. Heinz, Jan 22 2022

Mathematica

b[n_, t_] := b[n, t] = If[nJean-François Alcover, Apr 25 2022, after Alois P. Heinz *)

PARI

a(n) = my(N=2*n+1, m=N); while(m >= N, m = if (m%2, 3*m+1, m/2)); m; \\ Michel Marcus, Jan 22 2022

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 13 2001