A176356 Numbers which when seen in a mirror are primes (or 1), using calculator-style 7-segment numerals.

1, 2, 5, 10, 11, 20, 50, 100, 101, 110, 115, 118, 121, 125, 152, 158, 181, 185, 188, 200, 500, 1000, 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

Offset: 1

Author

P. Giannopoulos (pgiannop1(AT)yahoo.com), Apr 15 2010, Apr 22 2010

Keywords

• base
• easy
• nonn

Comments

We construct mirror images of numbers by placing a mirror parallel to the baseline at an acute angle and looking at them from the top of the sheet they are written on.

This defines the mirror images by fixing digits 0, 1 and 8, exchanging 2 and 5, reversing the order of the digits and ignoring leading zeros that may result.

Only entries of A080228 are admitted, because 3's, 4's, 6's, 7's and 9's do not have calculator style images.

If this combined operation on n generates an entry in A008578, n is in this sequence here.

Examples

			110 is in the sequence because the mirror is 011 = 11 and prime.
152 is in the sequence because the mirror is 521 = A000040(98), a prime.
31 is not in the sequence because the 3 cannot be mirrored.
115 is in the sequence because the mirror is 211 = A000040(47), a prime.
		

References

• P. Giannopoulos, The Brainteasers, unpublished.

Crossrefs

Cf. A080228, A080792, A008578

Programs

Maple

calcmirr := proc(n)
        local L,Lm,i ;
        L := convert(n,base,10) ;
        Lm := [] ;
        for i from 1 to nops(L) do
                if op(i,L) = 2 then
                        Lm := [5,op(Lm)] ;
                elif op(i,L) = 5 then
                        Lm := [2,op(Lm)] ;
                elif op(i,L) in {0,1,8} then
                        Lm := [op(i,L),op(Lm)] ;
                else
                        return 0 ;
                end if;
        end do:
        add(op(i,Lm)*10^(i-1),i=1..nops(Lm)) ;
end proc:
isA176356 := proc(n)
        local m;
        m := calcmirr(n) ;
        isprime(m) or (m = 1) ;
end proc:
for n from 1 to 2001 do
        if isA176356(n) then
                printf("%d,",n);
        end if;
end do: # R. J. Mathar, Sep 24 2011

PARI

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)
\\ Franklin T. Adams-Watters. Produces sequence except for initial 1

Extensions

Sequence reconstructed with a consistent interpretation of the definition. - R. J. Mathar, Sep 24 2011

Edited by N. J. A. Sloane, Oct 24 2011