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

2,1

Links

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

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 *)

Crossrefs

Cf. A002113.

Sequence in context: A051415 A037351 A293727 * A329254 A359003 A183296

Adjacent sequences: A077525 A077526 A077527 * A077529 A077530 A077531

Keyword

base,nonn,look

Author

Amarnath Murthy, Nov 08 2002

Extensions

Corrected and extended by Ray Chandler, Aug 20 2003

Status

approved