# [seqfan] Re: Product of digits touching the comma = first difference

Christopher Hunt gribble cgribble263 at btinternet.com
Wed Nov 9 01:05:11 CET 2011

```             Possible successors to V
1   2   3   4   5   6   7   8   9
V
1
2
3
4
5    10
6    12
7    14  21
8    16  24  32  40
9    18  27  36  45  54  63  72  81  90
10    10
11    12
12    14
13    16
14    18  22
15        25  30
16        28  34  40
17            38  45  52
18                    58  66  74  82  90
19
20        20
21        23
22        26
23        29  32
24            36  40
25                45  50
26                    56  62
27                        69  76  83  90
28
29
30            30
31            34
32            38  40
33                45
34                    54
35                        65  70
36                            78  84  90
37
38
39
40                40
41                45
42                    52
43                    58  61
44                        68  72
45                                85  90
46
47
48
49
50                    50
51                    56
52                        64
53                            74
54                                86  90
55
56
57
58
59
60                        60
61                        67
62                            76
63                                87  90
64
65
66
67
68
69
70                            70
71                            78
72                                88  90
73
74
75
76
77
78
79
80                                80
81                                89  90
82
83
84
85
86
87
88
89
90                                    90
91
92
93
94
95    100
96    102
97    104
98    106
99    108
100    100

Best regards,

Chris Gribble

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Eric Angelini
Sent: 08 November 2011 12:08 PM
To: Sequence Fanatics Discussion list
Cc: Jean-Marc Falcoz; Alexandre Wajnberg
Subject: [seqfan] Product of digits touching the comma = first difference

Hello SeqFans,

S = 96, 102, 104, 108, 116, 122, 124, 128, 136,
142, 144, 148, 156, 162, 164, 168, 176, 182,
184, 188, 196, 208, 216, 228, 244, 252, 256,
268, 284, 292, 296, 314, ...

The first difference between two adjacent integers is the product of the
digits touching the comma:

S = 96, 102, 104, 108, 116, 122, 124, 128, 136,
dif    6    2    4    8    6    2    4    8

Is 96 the smallest integer producing an infinite such sequence? (96 has no
predecessor.)

Note that 9, for instance, has 8 possible succes- sors (18,27,36... 81) --
18 itself having 5 pos- sible successors (58,66,74,82,90).

384 has two possible successors (396 and 400).

Integers ending with zero loop on themselves:
10,10,10,...

If 96 doesn't produce an infinite sequence, is there an integer which does?

Best,
É.

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

```