|
%I #16 Dec 01 2014 01:55:24
%S 0,1,2,3,4,5,7,14,80,160,301,602,693,994,1295,1627,1777,2365,2666,
%T 5296,5776,6256,17360,34720,51301,52201,105092,155493,209284,587846,
%U 735644,7904800,11495701,80005507,80469907,83165017,89731777,90196177
%N Palindromic in bases 6 and 15.
%C Intersection of A029953 and A029960.
%H Ray Chandler and Chai Wah Wu, <a href="/A249155/b249155.txt">Table of n, a(n) for n = 1..71</a> (terms < 6^28). First 65 terms from Ray Chandler.
%H Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On Simultaneous Palindromes</a>, arXiv:1403.0787 [math.NT]
%e 301 is a term since 301 = 1221 base 6 and 301 = 151 base 15.
%t palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; Select[Range[10^6] - 1, palQ[#, 6] && palQ[#, 15] &]
%o (Python)
%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): # generator of palindromes in base b of length <= 2*l
%o ....if l > 0:
%o ........yield 0
%o ........for x in range(1,l+1):
%o ............for y in range(b**(x-1),b**x):
%o ................s = digits(y,b)
%o ................yield int(s+s[-2::-1],b)
%o ............for y in range(b**(x-1),b**x):
%o ................s = digits(y,b)
%o ................yield int(s+s[::-1],b)
%o A249155_list = [n for n in palQgen(8,6) if palQ(n,15)] # _Chai Wah Wu_, Nov 29 2014
%Y Cf. A007632, A060792, A249156, A249157, A249158.
%K nonn,base
%O 1,3
%A _Ray Chandler_, Oct 27 2014
|
