Search: id:A079933
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%I A079933
%S A079933 1,2,5,7,11,12,19,22,27,33,37,39,42,44,53,54,60,62,68,69,75,77,78,83,86,
%T A079933 87,91,94,97,100,101,105,106,110,113,115,116,120,121,125,129,131,132,
%U A079933 137,141,144,148,149,152,155,157,166,171,173,178,179,184,186,189,191
%N A079933 Greedy powers of (1/sqrt(3)): sum_{n=1..inf} (1/sqrt(3))^a(n) = 1.
%C A079933 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.
%F A079933 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/sqrt(3)) and frac(y) = y - floor(y).
%e A079933 a(3)=5 since (1/sqrt(3)) + (1/sqrt(3))^2 + (1/sqrt(3))^5 < 1 and (1/sqrt(3)) 
               +(1/sqrt(3))^2 + (1/sqrt(3))^4 > 1; since the power 4 makes the sum 
               > 1, then 5 is the 3th greedy power of (1/sqrt(3)).
%Y A079933 Cf. A076796-A076802, A077468 - A077475, A079930 - A079932.
%Y A079933 Sequence in context: A025062 A175034 A030498 this_sequence A075610 A057922 
               A113543
%Y A079933 Adjacent sequences: A079930 A079931 A079932 this_sequence A079934 A079935 
               A079936
%K A079933 easy,nonn
%O A079933 1,2
%A A079933 Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003

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