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The Blatant Functions

Everybody knows the Fibonacci Function, which in its symbolic form goes like this:

with a,b=1 giving [1,1,2,3,5,8,13 …]. So there is a rucursion rule that goes fib(n)=fib(n-2)+fib(n-1) with fib(1)=1 and fib(2)=1. So the rule is constant. But what happens if we allow the recursion to rewrite the rule?

I call this the Blatant Function, cause I did not find this number sequence on internet. So this is:

with a,b=1 giving [1,1,2,3,8,49,1663,1777801,...]. Here the rule is rewritten every time with the result of the rule applied one step before. This means blatant(3)=blatant(1)+blatant(2), blatant(4)=blatant(3) applied to (blatant(2),blatant(3)) aso. This is realy a blatant function. The size of the numbers grows nearly with doubeling every step. So here are the sizes for the first 15 blatants: 1, 1, 1, 2, 4, 7, 13, 25, 49, 98, 194, 388, 775, 1550, 3099. Hm? ln(blatant(n)) is near bei 2**n and this is blatant.

And this is only the simplest blatant funcion, cause there is a infinite number of much more blatant blatant functions.

I think we should call this function ’’bla(n)’’. bla bla bla…