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

Eric Angelini Eric.Angelini at kntv.be
Tue Nov 8 13:07:33 CET 2011


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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