%I #3 Mar 30 2012 17:22:26
%S 1,3,13,38,41,54,57,60,63,67,73,75,88,91,95,98,101,109,116,122,125,
%T 129,131,142,145,151,159,163,169,172,176,190,200,205,210,215,217,228,
%U 235,241,250,252,266,271,276,280,283,296,298,311,315,318,323,326,329,334
%N Greedy powers of (e/4): sum_{n=1..inf} (e/4)^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/4) and frac(y) = y - floor(y).
%e a(4)=13 since (e/4) +(e/4)^3 +(e/4)^13 < 1 and (e/4) +(e/4)^3 +(e/4)^12 > 1; since the power 12 makes the sum > 1, then 13 is the 3rd greedy power of (e/4).
%p Digits := 400: summe := 0.0: p := evalf(exp(1)/4.): 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)
%E Corrected by _T. D. Noe_, Nov 02 2006
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