A079931 Greedy powers of (1/sqrt(Pi)): Sum_{n>=1} (1/sqrt(Pi))^a(n) = 1.

1, 2, 4, 8, 9, 16, 20, 22, 23, 32, 33, 36, 39, 42, 43, 46, 47, 50, 51, 55, 59, 60, 63, 69, 74, 77, 80, 82, 87, 92, 94, 97, 100, 102, 105, 107, 111, 113, 114, 117, 119, 122, 126, 128, 129, 134, 141, 142, 146, 147, 150, 151, 154, 157, 160, 162, 165, 167, 168, 171, 175

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..61.

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

Example

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

Crossrefs

Cf. A076796-A076802, A077468-A077475, A079930, A079932, A079933.

Sequence in context: A025611 A049439 A251642 * A188915 A055008 A204826

Adjacent sequences: A079928 A079929 A079930 * A079932 A079933 A079934

Keyword

easy,nonn

Author

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

Status

approved