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%I #1 May 16 2003 03:00:00
%S 1,2,3,16,17,20,22,24,26,29,31,32,34,38,40,43,44,46,48,50,52,53,57,58,
%T 60,61,64,66,67,69,70,75,76,80,83,85,87,90,91,93,95,101,102,106,107,
%U 110,118,126,129,130,134,135,138,142,143,145,146,149,151,154,156,161
%N Greedy powers of (e/5): sum_{n=1..inf} (e/5)^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=(e/5) and frac(y) = y - floor(y).
%e a(4)=16 since (e/5) +(e/5)^2 +(e/5)^3 + (e/5)^16 < 1 and (e/5) +(e/5)^2 +(e/5)^3 +(e/5)^15 > 1; since the power 15 makes the sum > 1, then 16 is the 4th greedy power of (e/5).
%p Digits := 400: summe := 0.0: p := evalf(exp(1)/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 Cf. A077468 - A077475.
%K easy,nonn
%O 1,2
%A Ulrich Schimke (ulrschimke(AT)aol.com)
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