A079933 Greedy powers of (1/sqrt(3)): sum_{n=1..inf} (1/sqrt(3))^a(n) = 1.

1, 2, 5, 7, 11, 12, 19, 22, 27, 33, 37, 39, 42, 44, 53, 54, 60, 62, 68, 69, 75, 77, 78, 83, 86, 87, 91, 94, 97, 100, 101, 105, 106, 110, 113, 115, 116, 120, 121, 125, 129, 131, 132, 137, 141, 144, 148, 149, 152, 155, 157, 166, 171, 173, 178, 179, 184, 186, 189, 191

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.

Links

Table of n, a(n) for n=1..60.

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

Example

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

Crossrefs

Cf. A076796-A076802, A077468-A077475, A079930-A079932.

Sequence in context: A175034 A030498 A355774 * A075610 A057922 A243047

Adjacent sequences: A079930 A079931 A079932 * A079934 A079935 A079936

Keyword

easy,nonn

Author

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

Status

approved