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A076802 Greedy powers of the gamma constant (0.577215664...) Sum_{n=1..infinity} (gamma)^a(n) = 1.

%I A076802 #10 Mar 08 2022 20:35:54
%S A076802 1,2,5,7,10,18,20,22,23,26,30,33,37,41,44,46,48,49,53,56,58,59,68,69,
%T A076802 75,77,78,81,88,90,94,96,98,100,102,105,106,109,111,116,120,122,124,
%U A076802 126,132,135,137,140,145,152,155,157,158,162,165,168,171,174,176,178
%N A076802 Greedy powers of the gamma constant (0.577215664...) Sum_{n=1..infinity} (gamma)^a(n) = 1.
%C A076802 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 A076802 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 = gamma and frac(y) = y - floor(y).
%e A076802 a(3)=5 since (gamma) + (gamma)^2 + (gamma)^5 < 1 and (gamma) + (gamma)^2 + (gamma)^4 > 1; the power 4 makes the sum > 1, so 5 is the 3rd greedy power of gamma.
%p A076802 Digits := 400: summe := 0.0: p := evalf(gamma): pexp := p: a := []: for i from 1 to 800 do: if summe + pexp < 1 then a := [op(a),i]: summe := summe + pexp: fi: pexp := pexp * p: od: a;
%Y A076802 Cf. A077468 - A077475.
%K A076802 easy,nonn
%O A076802 1,2
%A A076802 Ulrich Schimke (ulrschimke(AT)aol.com)
%E A076802 Corrected by _T. D. Noe_, Nov 02 2006