THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS

The equation  is used for a golden ratio family to calculate  for a range of values of a in the modular ring Z4.  The decimal part of ja is then used for x in the infinite series for which the associated sums are found. These lead to  a series of generalized Fibonacci sequences

ON GOLDBACH'S CONJECTURE

This paper considers some aspects of Goldbach's conjecture as a conjecture and estimates the number of prime pairs in some intervals in order to portray a compelling picture of some of the computational issues generated by the conjecture