%I #6 Apr 05 2014 09:59:19
%S 1,2,8,10,16,18,19,26,30,36,38,41,43,45,50,51,59,65,68,70,74,75,82,84,
%T 87,89,91,94,96,99,101,103,107,113,116,117,124,127,129,136,138,142,
%U 145,149,156,161,164,166,168,170,172,176,181,183,185,187,189,192,194,196
%N Greedy powers of (1/sqrt(e)): sum_{n=1..inf} (1/sqrt(e))^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(e)) and frac(y) = y - floor(y).
%e a(3)=8 since (1/sqrt(e)) + (1/sqrt(e))^2 + (1/sqrt(e))^8 < 1 and (1/sqrt(e)) + (1/sqrt(e))^2 + (1/sqrt(e))^7 > 1; the power 7 makes the sum > 1, so 8 is the 3rd greedy power of (1/sqrt(e)).
%Y Cf. A076796-A076802, A077468-A077475, A079931-A079933.
%K easy,nonn
%O 1,2
%A Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003