This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
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.
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
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
The sequence begins: 0, 0; 1, 1; 2, 5; 5, 2; 8, 8; 11, 11; 12, 51; 15, 21; 18, 81; 21, 15; 22, 55; 25, 25; 28, 85; ... 81 has its reflection as 18 in a mirror. 125 has its reflection as 251 in a mirror.
{0, 0}~Join~Array[If[Mod[#, 10] == 0, Nothing, If[IntegerLength[#1] == Length[#2], {#1, FromDigits@ #2}, Nothing] & @@ {#, Reverse@ IntegerDigits@ # /. {2 -> 5, 3 -> Nothing, 4 -> Nothing, 5 -> 2, 6 -> Nothing, 7 -> Nothing, 9 -> Nothing}}] &, 123] // Flatten (* Michael De Vlieger, Nov 05 2018 *)
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