A079932 Greedy powers of (1/sqrt(2)): sum_{n=1..inf} (1/sqrt(2))^a(n) = 1.

1, 4, 10, 13, 22, 27, 32, 36, 40, 49, 54, 62, 66, 71, 80, 91, 97, 102, 109, 114, 120, 124, 127, 138, 146, 149, 159, 165, 169, 180, 184, 187, 194, 202, 208, 219, 224, 231, 235, 248, 258, 263, 266, 274, 281, 287, 294, 300, 304, 308, 316, 323, 329, 337, 343, 350

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003

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)=10 since (1/sqrt(2)) + (1/sqrt(2))^4 + (1/sqrt(2))^10 < 1 and (1/sqrt(2)) + (1/sqrt(2))^4 + (1/sqrt(2))^9 > 1; the power 9 makes the sum > 1, so 10 is the 3rd greedy power of (1/sqrt(2)).
		

Crossrefs

Cf. A076796-A076802, A077468-A077475, A079930, A079931, A079933.

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(2)) and frac(y) = y - floor(y).