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%I #47 Dec 26 2022 13:00:37
%S 0,3,9,15,33,45,51,63,129,153,165,189,195,219,231,255,513,561,585,633,
%T 645,693,717,765,771,819,843,891,903,951,975,1023,2049,2145,2193,2289,
%U 2313,2409,2457,2553,2565,2661,2709,2805,2829,2925,2973,3069,3075,3171,3219,3315
%N List of binary palindromes of even length (written in base 10).
%C A178225(a(n)) = 1. - _Reinhard Zumkeller_, Oct 21 2011
%C a(n) is divisible by 3 and it is always an odd number for n > 0. Therefore a(n) is in A016945 for n > 0. - _Altug Alkan_, Dec 04 2015
%H Reinhard Zumkeller, <a href="/A048701/b048701.txt">Table of n, a(n) for n = 0..9999</a>
%F a(n) = (2^(floor_log_2(n)+1))*n + Sum_{i=0..floor_log_2(n)} '(bit_i(n, i)*(2^(floor_log_2(n)-i)))'.
%t Prepend[Select[Range@ 3315, Reverse@ # == # && EvenQ@ Length@ # &@ IntegerDigits[#, 2] &], 0] (* _Michael De Vlieger_, Dec 04 2015 *)
%o (Haskell)
%o a048701 n = foldr (\d v -> 2 * v + d) 0 (reverse bs ++ bs) where
%o bs = a030308_row (n)
%o -- _Reinhard Zumkeller_, Feb 19 2003, Oct 21 2011
%o (PARI) a048701(n) = my(f); f = length(binary(n)) - 1; 2^(f+1)*n + sum(i=0, f, bittest(n, i) * 2^(f-i)); \\ _Altug Alkan_, Dec 03 2015
%o (Python)
%o def A048701(n):
%o s = bin(n)[2:]
%o return int(s+s[::-1],2) # _Chai Wah Wu_, Feb 26 2021
%Y See also A048702 = this sequence divided by 3, A048700 = binary palindromes of odd length, A006995 = all binary palindromes, A048703 = quaternary (base 4) palindromes of even length.
%Y For first differences see A265026, A265027.
%Y Cf. A030308, A007088, A178225.
%K nonn,base
%O 0,2
%A _Antti Karttunen_, Mar 07 1999
%E Offset corrected by _Reinhard Zumkeller_, Oct 21 2011
%E Offset changed back to 0 by _Andrey Zabolotskiy_, Dec 26 2022
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