[seqfan] More hitters (Hofstadter)

Eric Angelini Eric.Angelini at kntv.be
Tue Feb 5 11:09:24 CET 2013


Hello Sedfans,
if we call "hofstadtering" the operation visible 
here http://oeis.org/A005228 we could indeed
hofstadter any integer to produce a strictly
increasing sequence.
Take 38, for instance and start a sequence S 
where S and the first differences together 
include all positive numbers exactly once:

S = 38   39   41   44   48   53   59   66   74   83 ...
d =    1    2    3    4    5    6    7    8    9

We see that 38 "hits" 83 (for instance) -- but
is 38 the smallest integer hitting 83? No, it
is 1 (as one will see following the above link).

What is the sequence of the "smallest hofstadter 
hitters" (SHH) of the natural numbers?

I guess SHH starts:

  n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
SHH = 1 2 1 3 4 3 1 5 6  4  3  1  7  8  5  4  7  1  9 10 ...

Best,
É.




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