A076797 Greedy powers of (Pi/5): Sum_{n>=1} (Pi/5)^a(n) = 1.

1, 3, 5, 8, 15, 17, 20, 25, 28, 30, 32, 35, 43, 54, 58, 65, 67, 70, 73, 76, 82, 86, 89, 94, 97, 100, 107, 112, 119, 121, 124, 130, 133, 135, 137, 141, 143, 146, 153, 156, 163, 166, 169, 175, 177, 180, 185, 195, 199, 204, 210, 212, 217, 220, 226, 229, 234, 239

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..58.

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 = Pi/5 and frac(y) = y - floor(y).

Example

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

Maple

Digits := 400: summe := 0.0: p := evalf(Pi / 5.): 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;

Crossrefs

Cf. A077468 - A077475.

Sequence in context: A095290 A080999 A077579 * A290630 A359851 A193147

Adjacent sequences: A076794 A076795 A076796 * A076798 A076799 A076800

Keyword

easy,nonn

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Extensions

Corrected by T. D. Noe, Nov 02 2006

Status

approved