Due to the succes of the classic equation f(x) = f(x-1) + f(x-2) and the recently discussed f(x) = f(x-1) + f(x/2) , I am in the mood to consider the generalization

f(x) = f(x-1) + f( exp^[k]( ln^[k](x) - ln[k](2) ) )

In particular

f(x) = f(x-1) + f( exp^[0.5]( ln^[0.5](x) - ln[0.5](2) ) )

and of course the similar ones ( 2sinh etc ).

Does f grow like exp^[0.5] ??

Maybe change the base to the golden mean ?

regards

tommy1729

f(x) = f(x-1) + f( exp^[k]( ln^[k](x) - ln[k](2) ) )

In particular

f(x) = f(x-1) + f( exp^[0.5]( ln^[0.5](x) - ln[0.5](2) ) )

and of course the similar ones ( 2sinh etc ).

Does f grow like exp^[0.5] ??

Maybe change the base to the golden mean ?

regards

tommy1729