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A080059 Greedy powers of (1/zeta(3)): sum_{n=1..inf} (1/zeta(3))^a(n) = 1, where 1/zeta(3) = .83190737258070746868... 2
1, 10, 26, 38, 54, 64, 80, 98, 115, 126, 136, 147, 158, 171, 181, 196, 206, 226, 243, 257, 267, 279, 293, 306, 324, 334, 355, 365, 378, 388, 398, 410, 432, 442, 455, 468, 491, 501, 519, 534, 545, 560, 572, 582, 593, 610, 628, 638, 650, 663, 672, 691, 704, 715 (list; graph; refs; listen; history; text; internal format)
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. A heuristic argument suggests that the limit of a(n)/n is m - sum_{n=m..inf} log(1 + x^n)/log(x) = 14.874449248373..., where x=(1/zeta(3)) and m=floor(log(1-x)/log(x))=9.

LINKS

Table of n, a(n) for n=1..54.

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/zeta(3)) and frac(y) = y - floor(y). See A077468 for mathematica program by Robert G. Wilson v.

EXAMPLE

a(3)=26 since (1/zeta(3)) +(1/zeta(3))^10 +(1/zeta(3))^26 < 1 and (1/zeta(3)) +(1/zeta(3))^10 +(1/zeta(3))^k > 1 for 10<k<26.

CROSSREFS

Cf. A077468, A080059.

Sequence in context: A245021 A045039 A322972 * A071348 A055042 A044071

Adjacent sequences:  A080056 A080057 A080058 * A080060 A080061 A080062

KEYWORD

nonn

AUTHOR

Benoit Cloitre and Paul D. Hanna, Jan 23 2003

STATUS

approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)