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A249157 Palindromic in bases 11 and 13.

%I A249157 #22 May 15 2025 10:38:32
%S A249157 0,1,2,3,4,5,6,7,8,9,10,12,84,366,510,732,876,1020,1098,1242,1464,
%T A249157 10248,30252,31110,62220,103704,146541,3382050,3698730,4391268,
%U A249157 225622530,272466250,413186676,713998530,801837204,848770222,912265732
%N A249157 Palindromic in bases 11 and 13.
%C A249157 Intersection of A029956 and A029958.
%H A249157 Ray Chandler, <a href="/A249157/b249157.txt">Table of n, a(n) for n = 1..69</a> (terms < 10^18)
%H A249157 Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On Simultaneous Palindromes</a>, arXiv:1403.0787 [math.NT], 2014.
%e A249157 366 is a term since 366 = 303 base 11 and 366 = 222 base 13.
%t A249157 palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,11]&&palQ[#,13]&]
%t A249157 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 *)
%o A249157 (Python)
%o A249157 from gmpy2 import digits
%o A249157 def palQ(n, b): # check if n is a palindrome in base b
%o A249157     s = digits(n, b)
%o A249157     return s == s[::-1]
%o A249157 def palQgen(l, b): # unordered generator of palindromes in base b of length <= 2*l
%o A249157     if l > 0:
%o A249157         yield 0
%o A249157         for x in range(1, b**l):
%o A249157             s = digits(x, b)
%o A249157             yield int(s+s[-2::-1], b)
%o A249157             yield int(s+s[::-1], b)
%o A249157 A249157_list = sorted([n for n in palQgen(6,11) if palQ(n,13)]) # _Chai Wah Wu_, Nov 25 2014
%Y A249157 Cf. A007632, A060792, A249155, A249156, A249158.
%K A249157 nonn,base
%O A249157 1,3
%A A249157 _Ray Chandler_, Oct 27 2014