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 A122953 a(n) = number of distinct positive integers represented in binary which are substrings of binary expansion of n. 11

%I

%S 1,2,2,3,3,4,3,4,4,4,5,6,6,6,4,5,5,5,6,6,5,7,7,8,8,8,8,9,9,8,5,6,6,6,

%T 7,6,7,8,8,8,8,6,8,10,9,10,9,10,10,10,10,11,10,10,11,12,12,12,12,12,

%U 12,10,6,7,7,7,8,7,8,9,9,8,7,9,10,10,11,11,10,10,10,10,11,9,7,11,11,13,13,12

%N a(n) = number of distinct positive integers represented in binary which are substrings of binary expansion of n.

%C a(n) = A078822(n) if n is of the form 2^k - 1. Otherwise, a(n) = A078822(n) - 1.

%C First occurrence of k: 1, 2, 4, 6, 11, 12, 22, 24, 28, 44, 52, 56, 88, 92, 112, 116, 186, 184, 220, 232, 244, 368, 376, 440, 472, ...,.

%C Last occurrence of k: 2^n -1.

%C a(n) = sum (A057427(A213629(n,k): k = 1 .. n). - _Reinhard Zumkeller_, Jun 17 2012

%H Jeremy Gardiner, <a href="/A122953/b122953.txt">Table of n, a(n) for n = 1..2000</a>

%e Binary 1 = 1, binary 2 = 10, binary 4 = 100 and binary 9 = 1001 are all substrings of binary 9 = 1001. So a(9) = 4.

%t f[n_] := Length@ Select[ Union[ FromDigits /@ Flatten[ Table[ Partition[ IntegerDigits[n, 2], i, 1], {i, Floor[ Log[2, n] + 1]}], 1]], # > 0 &]; Array[f, 90]

%o (Haskell)

%o import Data.List (isInfixOf)

%o a122953 n = length [x | x <- [1..n],

%o show (a007088 x) `isInfixOf` show (a007088 n)]

%o -- _Reinhard Zumkeller_, Jan 22 2012

%Y Cf. A078822.

%K nonn

%O 1,2

%A Leroy Quet Oct 25 2006

%E More terms from Robert G. Wilson v Nov 01 2006

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Last modified June 19 19:35 EDT 2013. Contains 226416 sequences.