A076801 Greedy powers of (e/5): sum_{n=1..inf} (e/5)^a(n) = 1.

1, 2, 3, 16, 17, 20, 22, 24, 26, 29, 31, 32, 34, 38, 40, 43, 44, 46, 48, 50, 52, 53, 57, 58, 60, 61, 64, 66, 67, 69, 70, 75, 76, 80, 83, 85, 87, 90, 91, 93, 95, 101, 102, 106, 107, 110, 118, 126, 129, 130, 134, 135, 138, 142, 143, 145, 146, 149, 151, 154, 156, 161

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• easy
• nonn

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.

Examples

			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).
		

Crossrefs

Cf. A077468 - A077475.

Programs

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;

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).