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A249158 Palindromic in bases 7 and 29.

%I A249158 #19 Sep 23 2024 14:17:59
%S A249158 0,1,2,3,4,5,6,8,16,24,150,300,5952,7752,7955,9755,9958,11904,13704,
%T A249158 13907,14110,15707,15910,392850,751043,4585544,12737804,12828748,
%U A249158 16380296,19289406,19380350,20228253,33115710,395849700,1339182534
%N A249158 Palindromic in bases 7 and 29.
%H A249158 Ray Chandler, <a href="/A249158/b249158.txt">Table of n, a(n) for n = 1..80</a> (terms < 10^18)
%H A249158 Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On Simultaneous Palindromes</a>, arXiv:1403.0787 [math.NT], 2014.
%e A249158 150 is a term since 150 = 303 base 7 and 150 = 55 base 27.
%t A249158 palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,7]&&palQ[#,29]&]
%o A249158 (Python)
%o A249158 from gmpy2 import digits
%o A249158 def palQ(n, b): # check if n is a palindrome in base b
%o A249158     s = digits(n, b)
%o A249158     return s == s[::-1]
%o A249158 def palQgen(l, b): # unordered generator of palindromes in base b of length <= 2*l
%o A249158     if l > 0:
%o A249158         yield 0
%o A249158         for x in range(1, b**l):
%o A249158             s = digits(x, b)
%o A249158             yield int(s+s[-2::-1], b)
%o A249158             yield int(s+s[::-1], b)
%o A249158 A249158_list = sorted([n for n in palQgen(8,7) if palQ(n,29)])
%o A249158 # _Chai Wah Wu_, Nov 25 2014
%Y A249158 Cf. A007632, A060792, A249155, A249156, A249157.
%K A249158 nonn,base
%O A249158 1,3
%A A249158 _Ray Chandler_, Oct 27 2014