A079930 Greedy powers of (1/sqrt(e)): sum_{n=1..inf} (1/sqrt(e))^a(n) = 1.

1, 2, 8, 10, 16, 18, 19, 26, 30, 36, 38, 41, 43, 45, 50, 51, 59, 65, 68, 70, 74, 75, 82, 84, 87, 89, 91, 94, 96, 99, 101, 103, 107, 113, 116, 117, 124, 127, 129, 136, 138, 142, 145, 149, 156, 161, 164, 166, 168, 170, 172, 176, 181, 183, 185, 187, 189, 192, 194, 196

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

Example

a(3)=8 since (1/sqrt(e)) + (1/sqrt(e))^2 + (1/sqrt(e))^8 < 1 and (1/sqrt(e)) + (1/sqrt(e))^2 + (1/sqrt(e))^7 > 1; the power 7 makes the sum > 1, so 8 is the 3rd greedy power of (1/sqrt(e)).

Crossrefs

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

Sequence in context: A336176 A329952 A073886 * A047467 A079599 A126002

Adjacent sequences: A079927 A079928 A079929 * A079931 A079932 A079933

Keyword

easy,nonn

Author

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

Status

approved