Search: id:A122953
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%I A122953
%S A122953 1,2,2,3,3,4,3,4,4,4,5,6,6,6,4,5,5,5,6,6,5,7,7,8,8,8,8,9,9,8,5,6,6,6,7,
%T A122953 6,7,8,8,8,8,6,8,10,9,10,9,10,10,10,10,11,10,10,11,12,12,12,12,12,12,10,
%U A122953 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 A122953 a(n) = number of distinct positive integers represented in binary which 
               are substrings of binary expansion of n.
%C A122953 a(n) = A078822(n) if n is of the form 2^k - 1. Otherwise, a(n) = A078822(n) 
               - 1.
%C A122953 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 A122953 Last occurrence of k: 2^n -1.
%H A122953 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A122953 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 A122953 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]
%Y A122953 Cf. A078822.
%Y A122953 Sequence in context: A066412 A117119 A139141 this_sequence A128998 A137813 
               A003313
%Y A122953 Adjacent sequences: A122950 A122951 A122952 this_sequence A122954 A122955 
               A122956
%K A122953 nonn
%O A122953 1,2
%A A122953 Leroy Quet Oct 25 2006
%E A122953 More terms from Robert G. Wilson v Nov 01 2006

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