[seqfan] Re: A055387

[Sean A. Irvine]

But isn't that exactly what A225035 is ?

On Wed, 18 Jan 2023 at 15:38, Arthur O'Dwyer <arthur.j.odwyer at gmail.com>
wrote:

> On Tue, Jan 17, 2023 at 5:16 PM <israel at math.ubc.ca> wrote:
>
> > A055387 is "Prime numbers such that some permutation (possibly omitting
> > zeros) of digits is a prime." Well, the identity permutation of the
> digits
> > of a prime is always a prime, so maybe it means nontrivial permutation.
> > But
> > no: the Data starts with 2, 3, 5, 7, 11, which have no nontrivial
> > permutations of the digits. Should we perhaps remove those terms?
> >
>
> Yes. (I agree with your reasoning.)  And suggest adding the word "other":
> "some *other* permutation of their digits (possibly omitting leading
> zeroes) is a prime."
>
>
> > Also, is it any zeros that can be omitted, or leading zeros?
>
>
> It is permitted to permute "101" into "011" and then drop the leading zero.
> We know this because "101" is in the sequence, and the only permutations of
> those digits that exist are "101" (identity permutation), "110" (not
> prime), and "011".
> I don't know what it would mean to "drop *non*-leading zeroes" from a
> digit-string that *is already a free permutation* of the input string! Just
> permute the digits a little more to get the zero to the front, and then
> drop it.
>
> Alternatively, one could imagine *adding* a leading zero before permuting
> the digits of "(0)11" to produce "101"; under that interpretation "11"
> should remain in the sequence. But that logic is both (1) ugly and (2)
> insufficient to explain why the OP put "2, 3, 5, 7" in the sequence also.
>
>
> Here's a small Python program that could be added to the entry. It
> generates the expected output:
>
> [13, 17, 31, 37, 71, 73, 79, 97, 101, 103, 107, 109, 113, 127, 131, 137,
> 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 239, 241, 251,
> 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 359, 367,
> 373, 379, 389, 397].
>
> def is_a055387(x):
>
>   if sympy.isprime(x):
>
>     for perm in itertools.permutations(str(x)):
>
>       p = int(''.join(perm))
>
>       if (p != x) and sympy.isprime(p):
>
>         return True
>
>   return False
>
>
> print([x for x in range(400) if is_a055387(x)])
>
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