A248889 Palindromic in base 10 and 18.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 171, 323, 343, 505, 595, 686, 848, 1661, 2112, 3773, 23332, 46664, 69996, 262262, 583385, 782287, 859958, 981189, 1254521, 1403041, 1832381, 39388393, 54411445, 55499455, 88844888, 118919811, 191010191

Offset

1,3

Comments

a(54) > 10^12.

Links

M. Fiorentini and Chai Wah Wu, Table of n, a(n) for n = 1..68 a(n) for n = 1..53 from M. Fiorentini.

Example

848 in decimal is 2B2 in base 18, so 848 is in the sequence.
1661 in decimal is 525 in base 18, so 1661 is in the sequence.
1771 in decimal is 587 in base 18, which is not a palindrome, so 1771 is not in the sequence.

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:
    true;
end proc:
Base := 18;
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

palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Select[Range[0, 499], palindromicQ[#] && palindromicQ[#, 18] &] (* Alonso del Arte, Mar 21 2015 *)

Prog

(PARI) isok(n) = (n==0) || ((d = digits(n, 10)) && (Vecrev(d) == d) && (d = digits(n, 18)) && (Vecrev(d) == d)); \\ Michel Marcus, Mar 14 2015
(Magma) [n: n in [0..2*10^7] | Intseq(n) eq Reverse(Intseq(n)) and Intseq(n, 18) eq Reverse(Intseq(n, 18))]; // Vincenzo Librandi, Mar 21 2015
(Python)
def palgen10(l): # generator of palindromes of length <= 2*l
....if l > 0:
........yield 0
........for x in range(1, l+1):
............n = 10**(x-1)
............n2 = n*10
............for y in range(n, n2):
................s = str(y)
................yield int(s+s[-2::-1])
............for y in range(n, n2):
................s = str(y)
................yield int(s+s[::-1])
def palcheck(n, b): # check if n is a palindrome in base b
....s = digits(n, b)
....return s == s[::-1]
A248889_list = [n for n in palgen10(9) if palcheck(n, 18)]
# Chai Wah Wu, Mar 23 2015

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A028731, A097855, A248899

Sequence in context: A117057 A249516 A239090 * A029967 A029968 A097855

Adjacent sequences: A248886 A248887 A248888 * A248890 A248891 A248892

Keyword

nonn,base

Author

Mauro Fiorentini, Mar 05 2015

Status

approved