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=(1/sqrt(e)) and frac(y) = y - floor(y).
EXAMPLE
a(3)=8 since (1/sqrt(e)) + (1/sqrt(e))^2 + (1/sqrt(e))^8 < 1 and (1/sqrt(e)) + (1/sqrt(e))^2 + (1/sqrt(e))^7 > 1; the power 7 makes the sum > 1, so 8 is the 3rd greedy power of (1/sqrt(e)).
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003
STATUS
approved