[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):
http://www.cetteadressecomportecinquantesignes.com/Waterfalls.htm
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":
2012,2,1,3,4,3,4,7,7,14,8,...
... 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:
_____
1818,9,9,9,17,18,18,10
... but 2012 will never show.
Best,
É.
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