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%I #13 Nov 25 2014 22:52:11
%S 0,1,2,3,4,5,6,7,8,9,10,12,84,366,510,732,876,1020,1098,1242,1464,
%T 10248,30252,31110,62220,103704,146541,3382050,3698730,4391268,
%U 225622530,272466250,413186676,713998530,801837204,848770222,912265732
%N Palindromic in bases 11 and 13.
%C Intersection of A029956 and A029958.
%H Ray Chandler, <a href="/A249157/b249157.txt">Table of n, a(n) for n = 1..69</a> (terms < 10^18)
%H Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On Simultaneous Palindromes</a>, arXiv:1403.0787 [math.NT]
%e 366 is a term since 366 = 303 base 11 and 366 = 222 base 13.
%t palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,11]&&palQ[#,13]&]
%o (Python)
%o from gmpy2 import digits
%o def palQ(n,b): # check if n is a palindrome in base b
%o ....s = digits(n,b)
%o ....return s == s[::-1]
%o def palQgen(l,b): # unordered generator of palindromes in base b of length <= 2*l
%o ....if l > 0:
%o ........yield 0
%o ........for x in range(1,b**l):
%o ............s = digits(x,b)
%o ............yield int(s+s[-2::-1],b)
%o ............yield int(s+s[::-1],b)
%o A249157_list = sorted([n for n in palQgen(6,11) if palQ(n,13)]) # _Chai Wah Wu_, Nov 25 2014
%Y Cf. A007632, A060792, A249155, A249156, A249158.
%K nonn,base
%O 1,3
%A _Ray Chandler_, Oct 27 2014
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