A076802 Greedy powers of the gamma constant (0.577215664...) Sum_{n=1..infinity} (gamma)^a(n) = 1.

1, 2, 5, 7, 10, 18, 20, 22, 23, 26, 30, 33, 37, 41, 44, 46, 48, 49, 53, 56, 58, 59, 68, 69, 75, 77, 78, 81, 88, 90, 94, 96, 98, 100, 102, 105, 106, 109, 111, 116, 120, 122, 124, 126, 132, 135, 137, 140, 145, 152, 155, 157, 158, 162, 165, 168, 171, 174, 176, 178

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(3)=5 since (gamma) + (gamma)^2 + (gamma)^5 < 1 and (gamma) + (gamma)^2 + (gamma)^4 > 1; the power 4 makes the sum > 1, so 5 is the 3rd greedy power of gamma.
		

Crossrefs

Cf. A077468 - A077475.

Programs

Maple

Digits := 400: summe := 0.0: p := evalf(gamma): 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 = gamma and frac(y) = y - floor(y).

Extensions

Corrected by T. D. Noe, Nov 02 2006