Four 4's etc

[N. J. A. Sloane]

Dear Seq Fans
Remember the old problem of finding the numbers
that you can make using four 4's and the operations
+, -, *, /, ^., etc ?

The OEIS contains many sequences based on this type of problem,
submitted at different times by various people.
I've found the following (though I may have missed some):

A036057 A048183 A048249 A060315 A060316
A061310 A066409 A068520 A069765 A070960
A071115 A071313 A071314 A071603 A071794
A071819 A071848 A071905 A071985 A078405
A078413

I'm making an entry in the Index file (under "four 4's") linking these
together.  I thought you might be interested in seeing
all the different versions of this problem. Several of them 
need extending, for example the last one, which is a variation
on A078405, submitted the other day by Kit Vongmahadlek:

%I A078413
%S A078413 2,2,5,13
%N A078413 Smallest positive integer than cannot be obtained from
exactly n copies of n using parentheses and the operations +, -, /, *, ^ and concatenation.
%H A078413 <a href="http://www.research.att.com/~njas/sequences/Sindx_Fo.html#4x4">Index entries for similar sequences</a>
%e A078413 With three 3's one can form 1=(3/3)^3, 2=3-3/3, 3=3+3-3, 4=3+3/3, but not 5, so a(3)=5.
%e A078413 With four 4's one can get 1=44/44, 2=4/4+4/4, 3=4-(4/4)^4, 4=4+(4-4)^4, 5=4+(4/4)^4, 6=(4+4)/4+4, 7=44/4-4, 8=4+4+4-4, 9=4+4+4/4, 10=(44-4)/4, 11=(4/4) concatenate (4/4), 12=(44+4)/4, but not 13, so a(4)=13.
%Y A078413 Cf. A078405.
%K A078413 nonn,base,new,bref,more
%O A078413 1,1
%A A078413 njas, Dec 28 2002

All the best for 2003!

Neil Sloane

 Neil J. A. Sloane
 AT&T Shannon Labs, Room C233, 
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 Email: njas at research.att.com
 Office: 973 360 8415; fax: 973 360 8178
 Home page: http://www.research.att.com/~njas/