Search: id:A080059
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%I A080059
%S A080059 1,10,26,38,54,64,80,98,115,126,136,147,158,171,181,196,206,226,243,257,
%T A080059 267,279,293,306,324,334,355,365,378,388,398,410,432,442,455,468,491,
%U A080059 501,519,534,545,560,572,582,593,610,628,638,650,663,672,691,704,715
%N A080059 Greedy powers of (1/zeta(3)): sum_{n=1..inf} (1/zeta(3))^a(n) = 1, where 
               1/zeta(3) = .83190737258070746868...
%C A080059 The n-th greedy power of x, when 0.5 < x < 1, is the smallest integer 
               exponent a(n) that does not cause the power series sum_{k=1..n} x^a(k) 
               to exceed unity. A heuristic argument suggests that the limit of 
               a(n)/n is m - sum_{n=m..inf} log(1 + x^n)/log(x) = 14.874449248373..., 
               where x=(1/zeta(3)) and m=floor(log(1-x)/log(x))=9.
%F A080059 a(n)=sum_{k=1..n}floor(g_k) where g_1=1, g_{n+1}=log_x(x^frac(g_n) - 
               x) (n>0) at x=(1/zeta(3)) and frac(y) = y - floor(y). See A077468 
               for mathematica program by Robert G. Wilson v.
%e A080059 a(3)=26 since (1/zeta(3)) +(1/zeta(3))^10 +(1/zeta(3))^26 < 1 and (1/
               zeta(3)) +(1/zeta(3))^10 +(1/zeta(3))^k > 1 for 10<k<26.
%Y A080059 Cf. A077468, A080059.
%Y A080059 Sequence in context: A005278 A157075 A045039 this_sequence A071348 A055042 
               A044071
%Y A080059 Adjacent sequences: A080056 A080057 A080058 this_sequence A080060 A080061 
               A080062
%K A080059 nonn
%O A080059 1,2
%A A080059 Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), 
               Jan 23 2003

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