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%I #4 Apr 05 2014 09:59:58
%S 1,2,5,7,11,12,19,22,27,33,37,39,42,44,53,54,60,62,68,69,75,77,78,83,
%T 86,87,91,94,97,100,101,105,106,110,113,115,116,120,121,125,129,131,
%U 132,137,141,144,148,149,152,155,157,166,171,173,178,179,184,186,189,191
%N Greedy powers of (1/sqrt(3)): sum_{n=1..inf} (1/sqrt(3))^a(n) = 1.
%C 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 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 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; the power 4 makes the sum > 1, so 5 is the 3rd greedy power of (1/sqrt(3)).
%Y Cf. A076796-A076802, A077468-A077475, A079930-A079932.
%K easy,nonn
%O 1,2
%A Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003