Problem 53735. Easy Sequences 58: Curious Prime-Rational Functions
For some prime numbers p and q where
, a rational function R, is defined as follows:
. Using the output
, another rational function K, is defined:
. Finaly, using the output
, we define the function N:
; where the symbol "
", represents the integer part of the decimal expansion of the fraction k .
For example for
and
:
;
; since
,
.
And, for
and
:
;
; since
,
.
If
, and given an integer limit x, write a function that returns a sorted array of all unique values of n that are less than or equal to x.
-----------
HINT: Both R and K, are rational functions and expect exact rational fraction outputs. Therefore, please preserve numerators and denominators for R and K, and evaluate decimal expansions only when calculating the output of the function N.
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