A394627 Indices of records in A133420, the number of iterations to reach 1 under the 5x+1 map A133419.

1, 2, 4, 5, 10, 20, 23, 46, 47, 85, 95, 190, 380, 383, 766, 919, 1655, 2117, 3575, 5081, 6097, 6503, 10463, 12053, 24106, 28927, 39053, 46283, 92566, 93727, 111079, 133295, 172757, 230333, 414617, 447773, 628985, 909047, 1081877, 1993973, 2501213, 2881397

Offset

1,2

Comments

The 5x+1 map A133419 yields x/p if p is the least prime factor < 5 of x, or 5x+1 if there's no such p.

Links

Table of n, a(n) for n=1..42.

Example

The records are as follows:
   n | a(n) = starting value m | record value A133420(m) > A133420(k) for all k < m
 ----+-------------------------+---------------------------------------------------
   1 |             1           |   0
   2 |             2           |   1
   3 |             4           |   2
   4 |             5           |  14
   5 |            10           |  15
   6 |            20           |  16
   7 |            23           |  21
   8 |            46           |  22
   9 |            47           |  26
  10 |            85           |  29
  11 |            95           |  54
  12 |           190           |  55
  13 |           380           |  56
  14 |           383           |  95
  15 |           766           |  96
  16 |           919           |  99
  17 |          1655           | 102
  18 |          2117           | 109
  19 |          3575           | 112
  20 |          5081           | 113
  21 |          6097           | 116
  22 |          6503           | 120
 ... |           ...           | ...

Prog

(PARI) my(r=-1); for(n=1, oo, A133420(n)>r && print1(n", ")+r=A133420(n))

Crossrefs

Cf. A133419 (the 5x+1 map), A133420 (number of iterations to reach 1).

Sequence in context: A118551 A161706 A128401 * A018467 A035524 A018283

Adjacent sequences: A394624 A394625 A394626 * A394628 A394629 A394630

Keyword

nonn

Author

M. F. Hasler, Apr 08 2026

Status

approved