A077528 a(n) = smallest nontrivial (>1) palindrome == 1 (mod n).

3, 4, 5, 6, 7, 8, 9, 55, 11, 111, 121, 66, 99, 121, 33, 171, 55, 77, 101, 22, 111, 323, 121, 101, 131, 55, 141, 88, 121, 373, 33, 232, 171, 141, 181, 1111, 77, 313, 121, 575, 505, 44, 353, 181, 323, 424, 1441, 99, 101, 868, 313, 10601, 55, 111, 393, 343, 929, 414

Offset: 2

Author

Amarnath Murthy, Nov 08 2002

Keywords

• base
• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A002113.

Programs

Maple

f:= proc(n) local d, S,j,q,x0,t,r,x;
    for d from 2 do
      S[ceil(d/2)+1]:= {0}:
      for j from ceil(d/2) to 1 by -1 do
        if j = (d+1)/2 then q:= 10^(j-1)
        else q:= 10^(j-1)+10^(d-j)
        fi;
        if j = 1 then x0:= 1 else x0:= 0 fi;
        S[j]:= {seq(seq(x*q+s mod n, x=x0..9), s=S[j+1])};
      od;
      if member(1, S[1]) then
         t:= 1; r:= 0;
         for j from 1 to ceil(d/2) do
           if j = (d+1)/2 then q:= 10^(j-1) else q:= 10^(j-1)+10^(d-j) fi;
           if j = 1 then x0:= 1 else x0:= 0 fi;
           for x from x0 to 9 do
             if member(t - x*q mod n, S[j+1]) then
                r:= r + x*q;
                t:= t - x*q mod n;
                break
             fi
           od;
        od;
        return r
      fi
   od
end proc:
$3..9, seq(f(n),n=9..100); # Robert Israel, Dec 17 2019

Mathematica

With[{pals=Select[Range[2,11000],PalindromeQ]},Table[SelectFirst[pals,Mod[#,n]==1&],{n,2,60}]] (* Harvey P. Dale, Dec 03 2023 *)

Extensions

Corrected and extended by Ray Chandler, Aug 20 2003