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A076797 Greedy powers of (Pi/5): Sum_{n>=1} (Pi/5)^a(n) = 1.

%I A076797 #6 Apr 11 2021 16:13:11
%S A076797 1,3,5,8,15,17,20,25,28,30,32,35,43,54,58,65,67,70,73,76,82,86,89,94,
%T A076797 97,100,107,112,119,121,124,130,133,135,137,141,143,146,153,156,163,
%U A076797 166,169,175,177,180,185,195,199,204,210,212,217,220,226,229,234,239
%N A076797 Greedy powers of (Pi/5): Sum_{n>=1} (Pi/5)^a(n) = 1.
%C A076797 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 A076797 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 = Pi/5 and frac(y) = y - floor(y).
%e A076797 Pi/5 + (Pi/5)^3 + (Pi/5)^5 < 1 and Pi/5 + (Pi/5)^3 + (Pi/5)^4 > 1; since the power 4 makes the sum > 1, 5 is the 3rd greedy power of (Pi/5), so a(3)=5.
%p A076797 Digits := 400: summe := 0.0: p := evalf(Pi / 5.): 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 A076797 Cf. A077468 - A077475.
%K A076797 easy,nonn
%O A076797 1,2
%A A076797 Ulrich Schimke (ulrschimke(AT)aol.com)
%E A076797 Corrected by _T. D. Noe_, Nov 02 2006