A076799 Greedy powers of (e/3): Sum_{n>=1} (e/3)^a(n) = 1.

1, 24, 92, 140, 171, 199, 226, 251, 277, 320, 363, 391, 425, 449, 474, 500, 524, 548, 575, 632, 673, 777, 801, 836, 861, 903, 932, 959, 983, 1011, 1054, 1087, 1113, 1148, 1176, 1228, 1261, 1286, 1316, 1348, 1394, 1427, 1452, 1480, 1510, 1536, 1571, 1600

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..48.

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

Example

a(3)=92 since (e/3) + (e/3)^24 + (e/3)^92 < 1 and (e/3) +(e/3)^24 + (e/3)^91 > 1; since the power 91 makes the sum > 1, then 92 is the 4th greedy power of (e/3).

Maple

Digits := 1100: summe := 0.0: p := evalf(exp(1)/3.): pexp := p: a := []: for i from 1 to 3000 do: if summe + pexp < 1 then a := [op(a), i]: summe := summe + pexp: fi: pexp := pexp * p: od: a;

Prog

(PARI) default(realprecision, 99); s=1; Le3=1-log(3); for(i=1, 50, print1(a=if(i>1, log(s)\Le3, 1)", "); s-=exp(a*Le3)) \\ M. F. Hasler, Sep 28 2009

Crossrefs

Cf. A077468 - A077475.

Sequence in context: A256718 A233637 A179962 * A297540 A365191 A353326

Adjacent sequences: A076796 A076797 A076798 * A076800 A076801 A076802

Keyword

easy,nonn

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Extensions

Some terms corrected (replaced 67,3 with 673 and 153,6 with 1536) by M. F. Hasler, Sep 28 2009

Status

approved