On Some two way Classifications of Integers

Note on Some Additive Properties of Integers

Let A=2 .3 . . . p r , the product of consecutive primes, be sufficiently large . By elementary method we prove that the number of solutions of the congruence p2-q2 =-0 (mod A) with 0 < q < p < A is greater than 1 A 1 + 41og log A . But the integers of the form p 2-q 2 with 0 < q< p < A lie all between 0 and A', hence there exists a multiple of 4 say n(<,4") such that the number of solutions of...

On Some Variations of Two-Way Probabilistic Finite Automata Models

Rabin [M. Rabin, Probabilistic finite automata, Information and Control (1963) 230–245] initiated the study of probabilistic finite automata (pfa). Rabin’s work showed a crucial role of the gap in the error bound (for accepting and non-accepting computations) in the power of the model. Further work resulted in the identification of qualitatively different error models (onesided error, bounded a...

Some sequences of integers

What I want to describe is a kind of experimental mathematics, ideal for doing at times when honest thinking is not going well. The requirements are a small computer (pencil and paper suffice, though the calculations are tedious), and Neil Sloane’s “A Handbook of Integer Sequences” [15]. This book, a kind of hitch-hikers’ guide to the universe N”, consists mainly of a list of 2372 sequences of ...

Some Remarks on Prime Factors of Integers

Some Canonical Sequences of Integers

Extending earlier work of R Donaghey and P J Cameron we investigate some canon ical eigen sequences associated with transformations of integer sequences Several known sequences appear in a new setting for instance the sequences such as studied by T Tsuzuku H O Foulkes and A Kerber in connection with multiply transi tive groups are eigen sequences for the binomial transform Many interesting new ...