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%I #25 Jul 10 2021 04:21:06
%S 1,2,5,10,11,20,50,100,101,110,115,118,121,125,152,158,181,185,188,
%T 200,500,1000,1010,1012,1018,1022,1028,1051,1081,1082,1085,1100,1102,
%U 1105,1108,1115,1118,1121,1150,1180,1181,1201,1202,1210,1211,1225,1250,1255,1282,1285,1501,1502,1520,1522
%N Numbers which when seen in a mirror are primes (or 1), using calculator-style 7-segment numerals.
%C 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.
%C 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.
%C Only entries of A080228 are admitted, because 3's, 4's, 6's, 7's and 9's do not have calculator style images.
%C If this combined operation on n generates an entry in A008578, n is in this sequence here.
%D P. Giannopoulos, The Brainteasers, unpublished.
%e 110 is in the sequence because the mirror is 011 = 11 and prime.
%e 152 is in the sequence because the mirror is 521 = A000040(98), a prime.
%e 31 is not in the sequence because the 3 cannot be mirrored.
%e 115 is in the sequence because the mirror is 211 = A000040(47), a prime.
%p calcmirr := proc(n)
%p local L,Lm,i ;
%p L := convert(n,base,10) ;
%p Lm := [] ;
%p for i from 1 to nops(L) do
%p if op(i,L) = 2 then
%p Lm := [5,op(Lm)] ;
%p elif op(i,L) = 5 then
%p Lm := [2,op(Lm)] ;
%p elif op(i,L) in {0,1,8} then
%p Lm := [op(i,L),op(Lm)] ;
%p else
%p return 0 ;
%p end if;
%p end do:
%p add(op(i,Lm)*10^(i-1),i=1..nops(Lm)) ;
%p end proc:
%p isA176356 := proc(n)
%p local m;
%p m := calcmirr(n) ;
%p isprime(m) or (m = 1) ;
%p end proc:
%p for n from 1 to 2001 do
%p if isA176356(n) then
%p printf("%d,",n);
%p end if;
%p end do: # _R. J. Mathar_, Sep 24 2011
%o (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)
%o \\ _Franklin T. Adams-Watters_. Produces sequence except for initial 1
%Y Cf. A080228, A080792, A008578
%K base,easy,nonn
%O 1,2
%A P. Giannopoulos (pgiannop1(AT)yahoo.com), Apr 15 2010, Apr 22 2010
%E Sequence reconstructed with a consistent interpretation of the definition. - _R. J. Mathar_, Sep 24 2011
%E Edited by _N. J. A. Sloane_, Oct 24 2011
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