Autobiographical numbers revisited
Maximilian Hasler
maximilian.hasler at gmail.com
Tue Jun 17 16:05:35 CEST 2008
> Substring | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10 |
> Occurrences | 5 | 3 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 2 | --> 53110100002
> More such numbers:
> Substring | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10 |11 |
> Occurrences | 5 | 4 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 2 | 1 | --> 541011000021
this seems not very natural to me, since to be consistent, you should
then include all possible substrings, e.g. also "54", "41", "21" etc.
(at least up to a given length, say 2 digits) - why just stop at 11 ??
And also, you silently ignore the substrings "01", ... so in fact you
should not talk about "strings" since you consider numbers, not
strings.
A better justified alternative would be, IMHO, to go to other bases
(e.g. count hexadecimal digits using hexadecimal digits, etc.)
One maybe "interesting" non-base sequence would be:
a(n)=number of autobiographical numbers [in the original strict sense] in base n
Maximilian
PS:
A047841 should have kw "full" (I suppose, the b-file justifies this)
A138480 - the 3 additional terms could have been just a remark in
A046043, or vice versa ("3 last terms not allowed if "digit 10 etc" is
considered as nonsense")....
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