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A079931 Greedy powers of (1/sqrt(Pi)): Sum_{n>=1} (1/sqrt(Pi))^a(n) = 1.

%I A079931 #9 Apr 11 2021 01:28:06
%S A079931 1,2,4,8,9,16,20,22,23,32,33,36,39,42,43,46,47,50,51,55,59,60,63,69,
%T A079931 74,77,80,82,87,92,94,97,100,102,105,107,111,113,114,117,119,122,126,
%U A079931 128,129,134,141,142,146,147,150,151,154,157,160,162,165,167,168,171,175
%N A079931 Greedy powers of (1/sqrt(Pi)): Sum_{n>=1} (1/sqrt(Pi))^a(n) = 1.
%C A079931 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 A079931 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(Pi)) and frac(y) = y - floor(y).
%e A079931 a(3)=4 since (1/sqrt(Pi)) + (1/sqrt(Pi))^2 + (1/sqrt(Pi))^4 < 1 and (1/sqrt(Pi)) + (1/sqrt(Pi))^2 + (1/sqrt(Pi))^3 > 1; the power 3 makes the sum > 1, so 4 is the 3rd greedy power of (1/sqrt(Pi)).
%Y A079931 Cf. A076796-A076802, A077468-A077475, A079930, A079932, A079933.
%K A079931 easy,nonn
%O A079931 1,2
%A A079931 Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003