A121760/1: two (interesting?) sequences

[Dean Hickerson]

Neil Sloane wrote:

> Franklin said:
> There are a couple of borderline cases: if we are looking only at the 
> final digit (or the digital root), is that base, or just modulus?
>
> Me:   that is base-dependent, so it would get the keyword base

There are many exceptions to that.  E.g.

    A002144, Pythagorean primes: primes of form 4n+1

could be defined as "primes with last digit 1 in base 4", but it doesn't
have the base keyword.  Neither do:

    A030430, Primes of form 10n+1
    A030431, Primes of form 10n+3
    A030432, Primes of form 10n+7
    A030433, Primes of form 10n+9
    A045465, Primes congruent to {0, 1} mod 7
    A045392, Primes congruent to {2} mod 7
    A045437, Primes congruent to 3 mod 7

The sequences

    A061237, Prime numbers == 1 (mod 9)
    A061238, Prime numbers == 2 (mod 9)
    A061239, Prime numbers == 4 (mod 9)
    A061240, Prime numbers == 5 (mod 9)
    A061241, Prime numbers == 7 (mod 9)
    A061242, Prime numbers == 8 (mod 9)

do have the base keyword, but I don't think they should.

Dean Hickerson
dean at math.ucdavis.edu