[seqfan] Re: A055387

[Allan Wechsler]

In situations like this, OEIS tradition is to respect the primacy of the
data. That is, in a situation where we know that either the description or
the data is wrong (because the description does not correctly describe the
data), editors tend to correct the description rather than the data.

This leads us to wonder what description could give rise to the data in
A055387. I think that the given description works *except *for the fact
that primes consisting of all the same digit (like 2, 3, 5, 7, and 11) get
a free pass. That is, if a prime can be permuted into a different prime, we
include it; and if it cannot be permuted at all we also include it.

The verbiage about 0 seems almost unnecessary to me. All it means is that
one is allowed to permute 0s to the most-significant end. That's what I
would have assumed even if nothing had been said about it.

On Tue, Jan 17, 2023 at 9:56 PM Sean A. Irvine <sairvin at gmail.com> wrote:

> 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)])
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>