[seqfan] "Printer's errors" sequences

Eric Angelini Eric.Angelini at kntv.be
Tue Feb 17 17:37:51 CET 2009

Hellon SeqFans,

Three sequences are now dealing with "Printer's errors" (if
I'm not wrong):

1) http://www.research.att.com/~njas/sequences/A096298

... is the first one, with this description (and comment) :

--> Numbers, not ending with 0, that are "printer's errors".
    Numbers n with property that they can be written as
    n = a^b*c^d*e^f*... and if all the multiplication and
    exponentiation signs are deleted then abcdef... is the 
    same decimal number. The final multiplicand in the product,
    uniquely, may or may not include an explicit exponent.

(I personally don't understand this very last remark)

2) http://www.research.att.com/~njas/sequences/A116890

--> "Printer's errors" of second kind (trivial multiples of
    10 omitted)
    Numbers n=abcde... that can be written as n = a*b^c*d^e...,
    where the last operation can be either a multiplication
    or an exponentiation. Cf. with A096298 where the first
    operation is an exponentiation.

(Again, this is not easy to understand in a glimpse -- at
least for me)

3) http://www.research.att.com/~njas/sequences/A156322

--> Integers N such that if you insert between each of their
    digits either "*" (times) or "^" (exponentiation), or 
    "nothing" (so that two or more digits form a substring 
    integer), you can get back N in a non trivial way (only 
    exception : two "^" mustn't be side by side, you don't
    want decompositions with a^b^c).

This last link (author: Jean-Marc Falcoz) has a way to see 
the problem that I prefer to the others:

a) there are no "first kind" or "second kind" printer's er-
rors -- they all fit in this seq. with the "insertion" idea

b) you don't see in Jean-Marc's seq. "horrors" like:
   170471 = 1*7^04*71
   1740725 = 1*7^4*0725
   ... where an exponent > 0 has a leading zero, or where
   a multiplicand has a leading zero

What do you think? Shouldn't those three seq. be merged 
in a new, complete and better defined one? I like the
general concept of "Printer's error"...

My two (euro)cents,

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