%N Bases of plain and extended interbase translation of 234099253 to a new prime number in base 10.
%C These are the bases for A217673(4) (shown through the first case for which prime iterations reach a single digit), that sequence's example. A217680 gives the number of times translation gives primes and fuller detail. 10 itself (and large bases that would not change the number) is (are) excluded. Normal interbase translation is done by taking a smaller base's representation of a number and reads it as though the number were actually represented in a larger one, so here 'extended' signifies that 'digits' may be permitted to be more than 9.
%e 234099253=47*170^3+110*170^2+54*170+73, and 47*10^3+110*10^2+54*10+73=58613, a prime; so 170 is included. This is the first base that reaches a prime smaller than it by iteration, with 58613 becoming 373 and 373 becoming 53.
%Y Cf. A217673, A217680.
%A _James G. Merickel_, Oct 10 2012