# [seqfan] Re: mirror numbers in A176356

franktaw at netscape.net franktaw at netscape.net
Fri Sep 23 22:40:25 CEST 2011

```The mirror is in a plane parallel to the one the numbers are in. This
produces the interchange of 2 and 5, and the reversal of the digits,
with 0, 1, and 8 fixed.

On the other hand, the test for primality seems to have failed almost
completely. We should not have 1, 10, 100; and we should have 5, 11,
50, 101, 110, 115, etc.

That's how it looks to  me, anyhow.

Using PARI program:

isa(n)=local(r,d);while(n>0,d=n%10;if(d==2,d=5,if(d==5,d=2,if(d==3||d==4|
|d==6||d==7||d==9,return(0))));r=r*10+d;n\=10);isprime(r)

I get (up to 10000):

2, 5, 11, 20, 50, 101, 110, 115, 118, 121, 125, 152, 158, 181, 185,
188, 200, 500, 1010, 1012, 1018, 1022, 1028, 1051, 1081, 1082, 1085,
1100, 1102, 1105, 1108, 1115, 1118, 1121, 1150, 1180, 1181, 1201, 1202,
1210, 1211, 1225, 1250, 1255, 1282, 1285, 1501, 1502, 1520, 1522, 1525,
1528, 1555, 1558, 1580, 1582, 1588, 1802, 1805, 1808, 1810, 1811, 1822,
1828, 1850, 1852, 1855, 1880, 1882, 2000, 5000,

-----Original Message-----
From: Richard Mathar <mathar at strw.leidenuniv.nl>

It would be nice if someone could provide a coherent explanation
or construction of http://oeis.org/A176356 .
i) It seems the author accepts 1 as a prime.
ii) The mirror operation appears to swap the role of 2 and 5
(why 2 is in the sequence but 5 not remains obscure...)
iii) The mirror operation may also reverse the digits, like a point
mirror but
not a plane mirror (?) This is probably needed to remove