[seqfan] Re: Multiplying waterfalls (and adding?)

Eric Angelini Eric.Angelini at kntv.be
Tue Mar 27 13:41:09 CEST 2012

>Hello SeqFans,
>Start S with a(1) > 9
>Now a(n) is simply the result of a multiplication :
>[the (n-1)th digit of S] x [the n-th digit of S]

A few results are now visible there (thanks to 
Hans Havermann and Maximilian Hasler):

Playing with the same idea, bud adding instead of
multiplying -- and starting with a(1)=0 and a(2)=1,
one would get:
S = 0,1,1,2,3,5,8,13,9,4,12,13,5,3,3,4,8,8,6,7,12,16,14,13,8,3,3,7,7,5,5,4,11,11,6,10,...
(the last computed term so far ("10") is the sum of
the 3 and 7 being "overlined". Should this sequence
enter the OEIS?

Every integer has its own such "signature":
... We might look for integers which "appear in 
their own signature" (meaning that we accept to 
concatenate a few neighboring digits). 1818 does
the job, for instance:

... but 2012 will never show.             

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