A '''Curzon number''' is defined to be a positive integer '''n''' for which '''2<sup>n</sup> + 1''' is evenly divisible by  '''2 × n + 1'''.

'''Generalized Curzon numbers''' are those where the positive integer '''n''', using a base integer '''k''', satisfy the condition that '''k<sup>n</sup> + 1''' is evenly divisible by  '''k × n + 1'''.

''Base here does not imply the radix of the counting system; rather the integer the equation is based on. All calculations should be done in base 10.'' 

Generalized Curzon numbers only exist for even base integers. 


;Task 

* Find and show the first '''50 Generalized Curzon numbers''' for even base integers from '''2''' through '''10'''.


;Stretch

* Find and show the '''one thousandth'''.


;See also

;* [https://www.numbersaplenty.com/set/Curzon_number Numbers Aplenty - Curzon numbers]
;* [[oeis:A224486|OEIS:A224486 - Numbers k such that 2*k+1 divides 2^k+1]] (Curzon numbers)

''and even though it is not specifically mentioned that they are Curzon numbers:''

;* [[oeis:A230076|OEIS:A230076 - (A007521(n)-1)/4]] (Generalized Curzon numbers with a base 4)
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