Hello Maximilian,
- why just stop at 11 ??
... because this is how A046043 works ! A046043 starts with array of length 1 (no integer) then 2 (no integer) then 3 (no integer) then 4 (2 integers, 1210, 2020) then 5 (1 integer, 21200) etc.
go to other bases
... ah yes, good idea. Best, É. -----Message d'origine----- De : Maximilian Hasler [mailto:maximilian.hasler@gmail.com] Envoyé : mardi 17 juin 2008 16:06 À : Eric Angelini Cc : SeqFan Objet : Re: Autobiographical numbers revisited
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")....