OFFSET
1,2
COMMENTS
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.
FORMULA
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/6) and frac(y) = y - floor(y).
EXAMPLE
a(4)=5 since (Pi/6) +(Pi/6)^2 +(Pi/6)^3 +(Pi/6)^5 < 1 and (Pi/6) +(Pi/6)^2 +(Pi/6)^3 +(Pi/6)^4 > 1; since the power 4 makes the sum > 1, then 5 is the 4th greedy power of (Pi/6).
MAPLE
Digits := 400: summe := 0.0: p := evalf(Pi / 6.): 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;
MATHEMATICA
g[1] = 1; g[n_] := g[n] = With[{x = Pi/6}, Log[x, x^FractionalPart[g[n-1]] - x]]; a[n_] := Sum[Floor[g[k]], {k, 1, n}]; Table[a[n], {n, 1, 64}] (* Jean-François Alcover, Jul 08 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
EXTENSIONS
Corrected by T. D. Noe, Nov 02 2006
STATUS
approved