The n-th term of this sequence is the result of forming an ASCII (American Standard Code for Information Exchange) text string of n characters using the (printable) character with the largest binary value and then converting the binary value of the string to base 10. a(n) is therefore a measure of the largest possible size of an ASCII string with n printable characters. This sequence uses standard 7-bit ASCII;
A175824 is the same sequence using 8-bit Extended ASCII.
Conjecture: For every a(n) there exists a sequence of primes (p(1), p(2), p(3), ...) such that for each term a(n) there exists a set of primes that when added to the term result in another prime. For example, a(2)=126 and 126 + {5,11,13,23,37,41,47,...} all are primes.
Corollary 1: If it is the case that the size of the set of prime numbers is countably infinite, then the cardinality of the sequence that contains the sequence of primes p(1), p(2), ... that produce a new prime for every a(n) is uncountably infinite ... [ (a(1)+p(1), a(1)+p(2), a(1)+p(3), ...), (a(2)+p(1)', a(2)+p(2)', a(2)+p(3)'), ...)
