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=(e/5) and frac(y) = y - floor(y).
EXAMPLE
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).
MAPLE
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;
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
STATUS
approved