A076800 Greedy powers of (e/4): sum_{n=1..inf} (e/4)^a(n) = 1.

1, 3, 13, 38, 41, 54, 57, 60, 63, 67, 73, 75, 88, 91, 95, 98, 101, 109, 116, 122, 125, 129, 131, 142, 145, 151, 159, 163, 169, 172, 176, 190, 200, 205, 210, 215, 217, 228, 235, 241, 250, 252, 266, 271, 276, 280, 283, 296, 298, 311, 315, 318, 323, 326, 329, 334

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)=13 since (e/4) +(e/4)^3 +(e/4)^13 < 1 and (e/4) +(e/4)^3 +(e/4)^12 > 1; since the power 12 makes the sum > 1, then 13 is the 3rd greedy power of (e/4).
		

Crossrefs

Cf. A077468 - A077475.

Programs

Maple

Digits := 400: summe := 0.0: p := evalf(exp(1)/4.): 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/4) and frac(y) = y - floor(y).

Extensions

Corrected by T. D. Noe, Nov 02 2006