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/3) and frac(y) = y - floor(y).
EXAMPLE
a(3)=92 since (e/3) + (e/3)^24 + (e/3)^92 < 1 and (e/3) +(e/3)^24 + (e/3)^91 > 1; since the power 91 makes the sum > 1, then 92 is the 4th greedy power of (e/3).
MAPLE
Digits := 1100: summe := 0.0: p := evalf(exp(1)/3.): pexp := p: a := []: for i from 1 to 3000 do: if summe + pexp < 1 then a := [op(a), i]: summe := summe + pexp: fi: pexp := pexp * p: od: a;
PROG
(PARI) default(realprecision, 99); s=1; Le3=1-log(3); for(i=1, 50, print1(a=if(i>1, log(s)\Le3, 1)", "); s-=exp(a*Le3)) \\ M. F. Hasler, Sep 28 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
EXTENSIONS
Some terms corrected (replaced 67,3 with 673 and 153,6 with 1536) by M. F. Hasler, Sep 28 2009
STATUS
approved