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 = gamma and frac(y) = y - floor(y).
EXAMPLE
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.
MAPLE
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;
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
EXTENSIONS
Corrected by T. D. Noe, Nov 02 2006
STATUS
approved