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A048701
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List of binary palindromes of even length (written in base 10).
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10
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0, 3, 9, 15, 33, 45, 51, 63, 129, 153, 165, 189, 195, 219, 231, 255, 513, 561, 585, 633, 645, 693, 717, 765, 771, 819, 843, 891, 903, 951, 975, 1023, 2049, 2145, 2193, 2289, 2313, 2409, 2457, 2553, 2565, 2661, 2709, 2805, 2829, 2925, 2973, 3069, 3075, 3171, 3219, 3315
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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A178225(a(n)) = 1. - Reinhard Zumkeller, Oct 21 2011
a(n) is divisible by 3 and it is always an odd number for n > 1. Therefore a(n) is in A016945 for n > 1. - Altug Alkan, Dec 04 2015
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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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)))'.
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MATHEMATICA
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Prepend[Select[Range@ 3315, Reverse@ # == # && EvenQ@ Length@ # &@ IntegerDigits[#, 2] &], 0] (* Michael De Vlieger, Dec 04 2015 *)
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PROG
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(Haskell)
a048701 n = foldr (\d v -> 2 * v + d) 0 (reverse bs ++ bs) where
bs = a030308_row (n - 1)
-- Reinhard Zumkeller, Feb 19 2003, Oct 21 2011
(PARI) a048701(n) = my(f); f = length(binary(n-1)) - 1; 2^(f+1)*(n-1) + sum(i=0, f, bittest(n-1, i) * 2^(f-i)); \\ Altug Alkan, Dec 03 2015
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CROSSREFS
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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.
For first differences see A265026, A265027.
Cf. A030308, A007088, A178225.
Sequence in context: A099409 A002127 A061810 * A031159 A058039 A013581
Adjacent sequences: A048698 A048699 A048700 * A048702 A048703 A048704
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KEYWORD
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nonn,base
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AUTHOR
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Antti Karttunen, Mar 07 1999
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EXTENSIONS
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Offset corrected by Reinhard Zumkeller, Oct 21 2011
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STATUS
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approved
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