A249157 Palindromic in bases 11 and 13.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 84, 366, 510, 732, 876, 1020, 1098, 1242, 1464, 10248, 30252, 31110, 62220, 103704, 146541, 3382050, 3698730, 4391268, 225622530, 272466250, 413186676, 713998530, 801837204, 848770222, 912265732

Offset: 1

Author

Ray Chandler, Oct 27 2014

Keywords

• nonn
• base

Comments

Intersection of A029956 and A029958.

Examples

			366 is a term since 366 = 303 base 11 and 366 = 222 base 13.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..69 (terms < 10^18)
• Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Crossrefs

Cf. A007632, A060792, A249155, A249156, A249158.

Programs

Mathematica

palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,11]&&palQ[#,13]&]
Select[Range[0,44*10^5],AllTrue[IntegerDigits[#,{11,13}],PalindromeQ]&] (* The program generates the first 30 terms of the sequence. *) (* Harvey P. Dale, May 15 2025 *)

Python

from gmpy2 import digits
def palQ(n, b): # check if n is a palindrome in base b
    s = digits(n, b)
    return s == s[::-1]
def palQgen(l, b): # unordered generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, b**l):
            s = digits(x, b)
            yield int(s+s[-2::-1], b)
            yield int(s+s[::-1], b)
A249157_list = sorted([n for n in palQgen(6,11) if palQ(n,13)]) # Chai Wah Wu, Nov 25 2014