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

[Christopher Hunt gribble]

             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.





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