>
> At first glance the verb calcIdx is unobtainable, as the stepwise index
> is lost; the argument grows as a function of its previous states (i.e. it is
> a recurrence relation), so we cannot use the length of the argument. But
Ok, the verb I posted is a so called self expanding but controlled generator
I started with the recurrence relation:
rabS=:(([:$:_1+]),[:$:_2+])^:(1<])M.
And here's a decimal form using Fibonacci OLEIS A005203:
rabD=: ]`(([:$:_2+])+[:($:*2&[EMAIL PROTECTED])_1+])@.(1<]) M.
or
rabD1=: (([:$:_2+])+[:($:*2&[EMAIL PROTECTED])_1+])^:(1<]) M.
(n.b. fib from jwiki Essays/Fibonacci sequences)
rabD"0 i.10
0 1 2 5 22 181 5814 1488565 12194330294 25573364166211253
And Fibonacci is everywhere
fib"0 i.13
0 1 1 2 3 5 8 13 21 34 55 89 144
[EMAIL PROTECTED]"0 i.13
1 1 2 3 5 8 13 21 34 55 89 144 233
Number of one's in sequence:
now=:+/@rabS
Number of zero's:
noz=:[:+/[EMAIL PROTECTED]
noz"0 [1+i.13
0 1 1 2 3 5 8 13 21 34 55 89 144
now"0 [1+i.13
1 1 2 3 5 8 13 21 34 55 89 144 233
> then, it occured to me that one and only one 1 , is added at every step.
> So the definition of calcIdx is simply +/ . Therefore we obtain:
>
> zUr6 =: $:&1 0 : ((, 1 , 0 #~ 1 = ({~ +/))@:]^:[)
What can I say!
>
> Now, I personally find forms like u@:]^:[ unappealing. Usually I try to
> convert them into the equivalent x u&n y form. This is especially true
> when I also see a bound argument. In this case, the argument isn't bound,
> but it is defaulted. And losing the monad would also clean up the
> parenthesis mess a bit. But I leave the reforumlation as an exercise for
> the reader.
I'll give it a try :-)
Thanks Dan
=@@i
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