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A249158 Palindromic in bases 7 and 29. 4

%I

%S 0,1,2,3,4,5,6,8,16,24,150,300,5952,7752,7955,9755,9958,11904,13704,

%T 13907,14110,15707,15910,392850,751043,4585544,12737804,12828748,

%U 16380296,19289406,19380350,20228253,33115710,395849700,1339182534

%N Palindromic in bases 7 and 29.

%H Ray Chandler, <a href="/A249158/b249158.txt">Table of n, a(n) for n = 1..80</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 150 is a term since 150 = 303 base 7 and 150 = 55 base 27.

%t palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,7]&&palQ[#,29]&]

%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 A249158_list = sorted([n for n in palQgen(8,7) if palQ(n,29)])

%o # _Chai Wah Wu_, Nov 25 2014

%Y Cf. A007632, A060792, A249155, A249156, A249157.

%K nonn,base

%O 1,3

%A _Ray Chandler_, Oct 27 2014

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Last modified May 15 04:50 EDT 2021. Contains 343909 sequences. (Running on oeis4.)