A248899 Numbers that are palindromic in bases 10 and 19.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 666, 838, 1771, 432234, 864468, 1551551, 1897981, 2211122, 155292551, 330050033, 453848354, 467535764, 650767056, 666909666, 857383758, 863828368, 47069796074, 62558085526, 67269596276, 87161116178, 96060106069, 121791197121, 127673376721, 139103301931, 234595595432, 246025520642

Offset: 1

Author

Mauro Fiorentini, Mar 06 2015

Keywords

• base
• nonn

Comments

Next term > 10^12.

Examples

			838 = 262 in base 19.
		

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A248889.

Programs

Magma

[n: n in [0..2*10^7] | Intseq(n) eq Reverse(Intseq(n))and Intseq(n, 19) eq Reverse(Intseq(n, 19))]; // Vincenzo Librandi, Mar 08 2015

Maple

IsPalindromic := proc(n, Base)   local Conv, i;
   Conv := convert(n, base, Base);
for i from 1 to nops(Conv) / 2 do:
    if Conv [i] <> Conv [nops(Conv) + 1 - i] then
       return false:
    fi:
od:
return true;
end proc;
Base := 19;
A := [];
for i from 1 to 10^6 do:
   S := convert(i, base, 10);
   V := 0;
   if i mod 10 = 0 then
      next;
   fi;
   for j from 1 to nops(S) do:
      V := V * 10 + S [j];
   od:
   for j from 0 to 10 do:
      V1 := V * 10^(nops(S) + j) + i;
      if IsPalindromic(V1, Base) then
         A := [op(A), V1];
      fi;
   od:
   V1 := (V - (V mod 10)) * 10^(nops(S) - 1) + i;
   if IsPalindromic(V1, Base) then
      A := [op(A), V1];
   fi;
od:
sort(A);

Mathematica

palQ[n_, b_] := Block[{d = IntegerDigits[n, b]}, If[d == Reverse@ d, True, False]]; Select[Range[0, 10^6], And[palQ[#, 10], palQ[#, 19]] &] (* Michael De Vlieger, Mar 07 2015 *)
b1=10; b2=19; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10^7}]; lst (* Vincenzo Librandi, Mar 08 2015 *)

PARI

isok(n) = (n==0) || ((d = digits(n, 10)) && (Vecrev(d) == d) && (d = digits(n, 19)) && (Vecrev(d) == d)); \\ Michel Marcus, Mar 07 2015