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A090397 Number of terms in simple continued fraction for (3/2)^n. 1
1, 2, 2, 4, 2, 5, 7, 6, 10, 8, 8, 5, 8, 13, 7, 10, 13, 10, 11, 10, 14, 19, 15, 13, 12, 13, 16, 17, 15, 11, 17, 24, 21, 29, 23, 18, 23, 24, 26, 31, 28, 26, 29, 31, 24, 31, 28, 26, 20, 18, 18, 23, 30, 33, 36, 36, 31, 33, 38, 37, 35, 37, 29, 40, 43, 45, 39, 37, 40, 39, 42, 47, 41, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

FORMULA

Conjecture : a(n) is asymptotic to c*n where c=12*(log(2)/Pi)^2=log(2)*Levy's constant=0.58416081665664902187922697....

MATHEMATICA

Table[Length[ContinuedFraction[(3/2)^n]], {n, 0, 100}] (* G. C. Greubel, Mar 23 2017 *)

PROG

(PARI) a(n)=length(contfrac((3/2)^n))

CROSSREFS

Cf. A089729.

Sequence in context: A286280 A290088 A179013 * A328729 A329733 A289624

Adjacent sequences:  A090394 A090395 A090396 * A090398 A090399 A090400

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 31 2004

STATUS

approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)