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Natural numbers = Everything


1d
accepted How many ways can $n$ spaces be used with blocks of size $\le n$ (or leave empty)
Sep
24
awarded  Autobiographer
Sep
6
awarded  Popular Question
Jul
2
awarded  Curious
Jun
9
comment How many ways can $n$ spaces be used with blocks of size $\le n$ (or leave empty)
Although I would prefer to understand a proof/induction/whatever, it's anyway a good advice to search OEIS first! +1
Jun
9
comment How many ways can $n$ spaces be used with blocks of size $\le n$ (or leave empty)
+1 for induction, although I am not sure to agree in "1 way of using 0 spaces", (I think there is no way of using '0 spaces'), but leaving that case aside numbers seems to fit!
Jun
9
comment How many ways can $n$ spaces be used with blocks of size $\le n$ (or leave empty)
@JimmyK4542 yes you are right, edited
Jun
9
revised How many ways can $n$ spaces be used with blocks of size $\le n$ (or leave empty)
added 57 characters in body
Jun
9
asked How many ways can $n$ spaces be used with blocks of size $\le n$ (or leave empty)
Feb
21
accepted Consistent but incomplete formal axiomatic systems
Feb
21
comment How to change from base $n$ to $m$
I would like to know more about the distinction between "representations that mix", and that "don't mix" (or 'bleed' as you said) "i.e. blocks of digits can be considered without worrying about their neighbors", this reminds me prefix codes that can be decoded while reading, I see that if the conversion is made between power-relate-bases "block of digits" can be converted, but between non-related-to-power-bases the conversion seems to get complex, I wish this distinction would have a name, (better than bleed), it deserves one!
Feb
21
comment How to change from base $n$ to $m$
+1 for a different answer, great that you pointing out about m=n^k, it's hard for me to 'translate'your notation into code, but I will google for Horner form. Do you know any paper or related material on this kind of conversion? (I've asked a question about this fact here cs.stackexchange.com/questions/21736/…)
May
14
awarded  Caucus
May
10
accepted Clues to prove average in T is minor or equal than average in a smaller inner interval.
May
10
comment Clues to prove average in T is minor or equal than average in a smaller inner interval.
@user69810 added "or disprove", the thing is how to elaborate this kind of problems
May
10
comment Clues to prove average in T is minor or equal than average in a smaller inner interval.
@WimC good comment, thanks, fixed (I think)
May
10
revised Clues to prove average in T is minor or equal than average in a smaller inner interval.
added 1 characters in body
May
10
asked Clues to prove average in T is minor or equal than average in a smaller inner interval.
Mar
14
accepted Bounded recursive sequence
Mar
14
comment Bounded recursive sequence
Yes is a recurrence relation, I didn't knew about $2a_n=3a_{n-1}-2a_{n-2}$, I would have thought that it was a periodic function, is amazing, thanks