Search: id:A057716
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%I A057716
%S A057716 0,3,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,
%T A057716 29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U A057716 52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74
%N A057716 The non-powers of 2.
%C A057716 a(n) is the length signature of a string plus its length.
%C A057716 The positive members of this sequence are exactly the numbers that can 
               be expressed as the sum of two or more consecutive positive integers 
               (cf. A138591). - David Wasserman (wasserma(AT)spawar.navy.mil), Jan 
               24 2002
%C A057716 Starting at 3, these are the positions of the check bits in the single-error-correcting 
               Hamming code.
%C A057716 Except for the offset 0, sequence corresponds to numbers with at least 
               an odd divisor. (For largest odd divisor see A000265.) - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), Apr 12 2005
%C A057716 These are exactly the numbers n with the property that, given the n(n-1)/
               2 sums of pairs, the original numbers can be recovered uniquely. 
               [Nick Reingold, see Winkler reference.]
%C A057716 Subsequence of A158581; A000120(a(n)) > 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 16 2009]
%D A057716 P. Winkler, Mathematical Mind-Benders, Peters, Wellesley, MA, 2007; see 
               p. 27.
%H A057716 R. Zumkeller, <a href="b057716.txt">Table of n, a(n) for n = 0..10000</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 
               16 2009]
%F A057716 a(n) = n + [log_2(n + [log_2(n)])] gives this sequence with the exception 
               of a(1) = 1. - David W. Wilson, Mar 29 2005
%F A057716 Find k such that 2^k - (k + 1) <= n < 2^(k+1) - (k + 2), then a(n) = 
               n + k + 1.
%F A057716 Numbers n=2a(k)-1 k>0 are such that sum_{k=0...n}B_kM(n-k)binomial(n, 
               k)=0 where B_k is the k-th Bernoulli number and M_k the k-th Motzkin 
               number - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 19 2005
%Y A057716 Complement of A000079. Cf. A057717, A001227, A138591.
%Y A057716 See A074894 for more about the question of when the sums of n numbers 
               taken k at a time determine the numbers.
%Y A057716 Sequence in context: A010906 A114309 A079581 this_sequence A138591 A136492 
               A062506
%Y A057716 Adjacent sequences: A057713 A057714 A057715 this_sequence A057717 A057718 
               A057719
%K A057716 nonn
%O A057716 0,2
%A A057716 John Lindgren (john.lindgren(AT)Eng.Sun.COM), Oct 24 2000
%E A057716 Better description from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 
               29 2001

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