Search: id:A064896
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%I A064896
%S A064896 1,3,5,7,9,15,17,21,31,33,63,65,73,85,127,129,255,257,273,341,511,513,
%T A064896 585,1023,1025,1057,1365,2047,2049,4095,4097,4161,4369,4681,5461,8191,
%U A064896 8193,16383,16385,16513,21845,32767,32769,33825,37449,65535,65537
%N A064896 Numbers of the form (2^{mr}-1)/(2^r-1) for positive integers m, r.
%C A064896 Binary expansion of n consists of single 1's diluted by (possibly empty) 
               equal-sized blocks of 0's.
%C A064896 A064894(a(n)) = A056538(n)
%C A064896 According to Stolarsky's Theorem 2.1, all numbers in this sequence are 
               sturdy numbers; this sequence is a subsequence of A125121. - T. D. 
               Noe, Jul 21 2008
%D A064896 T. Chinburg and M. Henriksen, Sums of k-th powers in the ring of polynomials 
               with integer coefficients, Acta Arithmetica, 29 (1976), 227-250.
%H A064896 T. D. Noe, <a href="b064896.txt">Table of n, a(n) for n=1..1000</a>
%H A064896 K. B. Stolarsky, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa38/aa3825.pdf">
               Integers whose multiples have anomalous digital frequencies</a>, 
               Acta Arithmetica, 38 (1980), 117-128.
%e A064896 73 is included because it is 1001001 in binary, whose 1's are diluted 
               by blocks of two 0's.
%p A064896 f := proc(p) local m,r,t1; t1 := {}; for m from 1 to 10 do for r from 
               1 to 10 do t1 := {op(t1), (p^(m*r)-1)/(p^r-1)}; od: od: sort(convert(t1,
               list)); end; f(2); # very crude!
%Y A064896 A064894, A056538.
%Y A064896 Sequence in context: A121820 A006995 A163410 this_sequence A076188 A073674 
               A084722
%Y A064896 Adjacent sequences: A064893 A064894 A064895 this_sequence A064897 A064898 
               A064899
%K A064896 base,easy,nonn
%O A064896 1,2
%A A064896 Marc LeBrun (mlb(AT)well.com), Oct 11 2001

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