A394627 - OEIS

%I #10 Apr 14 2026 18:34:34

%S 1,2,4,5,10,20,23,46,47,85,95,190,380,383,766,919,1655,2117,3575,5081,

%T 6097,6503,10463,12053,24106,28927,39053,46283,92566,93727,111079,

%U 133295,172757,230333,414617,447773,628985,909047,1081877,1993973,2501213,2881397

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

%C 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.

%e The records are as follows:

%e    n | a(n) = starting value m | record value A133420(m) > A133420(k) for all k < m

%e  ----+-------------------------+---------------------------------------------------

%e    1 |             1           |   0

%e    2 |             2           |   1

%e    3 |             4           |   2

%e    4 |             5           |  14

%e    5 |            10           |  15

%e    6 |            20           |  16

%e    7 |            23           |  21

%e    8 |            46           |  22

%e    9 |            47           |  26

%e   10 |            85           |  29

%e   11 |            95           |  54

%e   12 |           190           |  55

%e   13 |           380           |  56

%e   14 |           383           |  95

%e   15 |           766           |  96

%e   16 |           919           |  99

%e   17 |          1655           | 102

%e   18 |          2117           | 109

%e   19 |          3575           | 112

%e   20 |          5081           | 113

%e   21 |          6097           | 116

%e   22 |          6503           | 120

%e  ... |           ...           | ...

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

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

%K nonn

%O 1,2

%A _M. F. Hasler_, Apr 08 2026