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A078822
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Number of distinct binary numbers contained as substrings in the binary representation of n.
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23
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1, 1, 3, 2, 4, 4, 5, 3, 5, 5, 5, 6, 7, 7, 7, 4, 6, 6, 6, 7, 7, 6, 8, 8, 9, 9, 9, 9, 10, 10, 9, 5, 7, 7, 7, 8, 7, 8, 9, 9, 9, 9, 7, 9, 11, 10, 11, 10, 11, 11, 11, 11, 12, 11, 11, 12, 13, 13, 13, 13, 13, 13, 11, 6, 8, 8, 8, 9, 8, 9, 10, 10, 9, 8, 10, 11, 11, 12, 12, 11, 11, 11, 11, 12, 10, 8
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OFFSET
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0,3
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COMMENTS
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For k>0: a(2^k-2)=2*(k-1)+1, a(2^k-1)=k, a(2^k)=k+2;
for k>1: a(2^k+1)=k+2;
for k>0: a(2^k-1)=A078824(2^k-1), a(2^k)=A078824(2^k).
For n>0: 0<a(2*n)-a(n)<=A070939(n)+1, 0<a(2*n+1)-a(n) < A070939(n). - Reinhard Zumkeller, Mar 07 2008
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 0..1000
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EXAMPLE
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n=10 -> '1010' contains 5 different binary numbers: '0' (b0bb or bbb0), '1' (1bbb or bb1b), '10' (10bb or bb10), '101' (101b) and '1010' itself, therefore a(10)=5.
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MATHEMATICA
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a[n_] := (id = IntegerDigits[n, 2]; nd = Length[id]; Length[ Union[ Flatten[ Table[ id[[j ;; k]], {j, 1, nd}, {k, j, nd}], 1] //. {0, b__} :> {b}]]); Table[ a[n], {n, 0, 85}] (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
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(Haskell)
import Numeric (showIntAtBase)
import Data.List (isInfixOf)
a078822 n = sum (map (fromEnum . (`isInfixOf` head bins)) bins) wher
bins = map (flip (showIntAtBase 2 ("01" !!)) "") [n, n-1..0]
-- Reinhard Zumkeller, Sep 14 2011
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CROSSREFS
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Cf. A078823, A078826, A078824, A007088, A144623, A144624.
Sequence in context: A128220 A134749 A061901 * A224980 A154392 A069745
Adjacent sequences: A078819 A078820 A078821 * A078823 A078824 A078825
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KEYWORD
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nonn,base,nice
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AUTHOR
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Reinhard Zumkeller, Dec 08 2002
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STATUS
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approved
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