A394628 Indices of records in A133422, the number of iterations to reach 1 under the 7x+1 map A133421.

1, 2, 4, 7, 11, 19, 31, 49, 53, 106, 121, 163, 283, 343, 403, 806, 1471, 1681, 1919, 3133, 4243, 4849, 8659, 11683, 12373, 24746, 30301, 35803, 71606, 76963, 105751, 155389, 239893, 479786, 509971, 1019942, 1109899, 1296043, 2039443, 4078886, 8157772, 9327623, 16582441

Offset

1,2

Comments

The 7x+1 map A133421 yields x/p if p = smallest prime factor < 7 of x, or 7x+1 if there's no such p.

Links

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

Formula

a(n+1) <= 2*a(n) with equality for n = 1, 2, 9, 15, 25, 28, 33, 35, 39, 40...

Example

The records are as follows:
   n | a(n) = starting value m | record value A133422(m) > A133422(k) for all k < m
 ----+-------------------------+---------------------------------------------------
   1 |             1           |   0
   2 |             2           |   1
   3 |             4           |   2
   4 |             7           |   4
   5 |            11           |  12
   6 |            19           |  21
   7 |            31           |  47
   8 |            49           |  50
   9 |            53           |  51
  10 |           106           |  52
  11 |           121           |  56
  12 |           163           |  58
  13 |           283           |  61
  14 |           343           |  85
  15 |           403           |  92
  16 |           806           |  93
  17 |          1471           | 105
  18 |          1681           | 109
  19 |          1919           | 115
  20 |          3133           | 122
  21 |          4243           | 127
 ... |           ...           | ...

Prog

(PARI) my(r=-1); for(n=1, oo, A133422(n)>r && print1(n", ")+r=A133422(n))
(Python)
def A394628(n):
    while len(T := A394628.T) < n:
        N = T[-1]+1; R = A133422(N-1)
        while A133422(N) <= R: N += 1
        T.append(N)
    return T[n-1]
A394628.T = [1]

Crossrefs

Cf. A394627 (same for P=5), A133421 (the 7x+1 map), A133422 (number of iterations to reach 1).

Sequence in context: A003292 A007864 A277271 * A192670 A118647 A000802

Adjacent sequences: A394625 A394626 A394627 * A394629 A394630 A394631

Keyword

nonn

Author

M. F. Hasler, Apr 08 2026

Status

approved