[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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