Odd and even bases are very different in both version 1 and version 2. For a number to be prime, it must be odd (or 2). A number in an odd base is odd when an odd number of its digits are odd.* In version 1, each pattern of odd & even digits is a separate equivalence class (assuming the class is connected). In version 2, the number of odd digits cannot change, so there are about length/2 classes (again assuming that the classes are connected). The prime 2 will add a little bit of extra connectivity, but not much. Rich * Make up a meaningful sentence with >4 occurrences of "odd". ------------------- Quoting "N. J. A. Sloane" <njas@research.att.com>:
I've seen two different versions of how you can move from one prime to another:
Version 1: change a single digit Version 2: change a single digit and then permute the digits
subject in both cases to the restriction that the new prime cannot begin with 0; the number of digits must remain constant.
Call two primes equivalent if you can go from one to the other in this way.
For each version of equivalence, there are four obvious sequences:
a(n) = number of equivalence classes of primes with n digits.
Arrange the equivalence classes by the size of the smallest member.
b(k) = size of the k-th equivalence class c(k) = smallest member of the k-th equivalence class d(k) = largest member of the k-th equivalence class
Presumably the two a-sequences will begin with a bunch of 1's, the two b-sequences will start like A006879, the two c-sequences will start like A003617, and the two d-sequences will start like A003618.
There are potentially eight (new?) sequences here - could someone compute them?
Thanks!
Neil
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