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A159780
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Inner product of the binary representation of n and its reverse.
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3
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0, 1, 0, 2, 0, 2, 1, 3, 0, 2, 0, 2, 0, 2, 2, 4, 0, 2, 0, 2, 1, 3, 1, 3, 0, 2, 2, 4, 1, 3, 3, 5, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 4, 2, 4, 0, 2, 2, 4, 0, 2, 2, 4, 0, 2, 2, 4, 2, 4, 4, 6, 0, 2, 0, 2, 0, 2, 0, 2, 1, 3, 1, 3, 1, 3, 1, 3, 0, 2, 0, 2, 2, 4, 2, 4, 1, 3, 1, 3, 3, 5, 3, 5, 0, 2, 2, 4, 0, 2, 2, 4, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) counts the number of 1's that coincide in the binary representation of n and its reverse. For the n in A140900, we have a(n)=0. The number k first appears at n=2^k-1.
Also central terms and right edge of the triangle in A173920: a(n)=A173920(2*n,n)=A173920(n,n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2010]
a(A000225(n)) = n and a(m) < n for m < A000225(n). [Reinhard Zumkeller, Oct 21 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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EXAMPLE
| 14 is represented by the binary vector (1,1,1,0). The reverse is (0,1,1,1). The inner product is 1*0+1*1+1*1+0*1 = 2. Hence a(14) = 2.
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MATHEMATICA
| Table[d=IntegerDigits[n, 2]; d.Reverse[d], {n, 0, 1023}]
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PROG
| (Haskell)
import Data.List (unfoldr)
a159780 n = sum $ zipWith (*) bin $ reverse bin where
bin = unfoldr
(\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2) n
-- Reinhard Zumkeller, Oct 21 2011
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CROSSREFS
| Sequence in context: A125942 A061986 A127185 * A138036 A055136 A074397
Adjacent sequences: A159777 A159778 A159779 * A159781 A159782 A159783
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Apr 22 2009
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